Answer:
![x1 = - (5)/(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/gnmdxb91ig3973vq3hcv3co5vgf31dq5gj.png)
![x2 = (4)/(3)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/fy7aksl0nnqny1wvl1g7hsvapdldy20mxb.png)
Explanation:
![18 {x}^(2) + 21x - 60 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/2iquh03s10korh2toulh9mupfs38k1c4b6.png)
Divide both sides of the equation by 3
![6 {x}^(2) + 7x - 20 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/k1s1y2uilpj84cz0edflcrmn6tyvnbbbf9.png)
Write 7x as a difference
![6 {x}^(2) + 15x - 8x - 20 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/io5t6exv13q8a8oteyu6ggcqtkhmyz4ty4.png)
Factor out 3x from the expression
![3x(2x + 5) - 8x - 20 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/kjybeqq0ri2dphb48l6zqmdm86q2scorio.png)
Factor out -4 from the expression
![3x(2x + 5) - 4(2x + 5) = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/b3tk34kxaa6bq3hs5h0yonuir98knqdnes.png)
Factor out 2x + 5 from the expression
![(2x + 5)(3x - 4) = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/vg02dknf9iijygslywnf6vn8hm6sryg2c9.png)
When the product of factors equals 0 , at least one factor is 0
![2x + 5 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/boz4b7iitt5bqapfxvmwoj9ttbh3stsh5r.png)
![3x - 4 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zp2p548vl4hzea53esmmgsicmitftle5o4.png)
Solve the equation for X
![2x + 5 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/boz4b7iitt5bqapfxvmwoj9ttbh3stsh5r.png)
Move constant to R.H.S and change its sign
![2x = 0 - 5](https://img.qammunity.org/2021/formulas/mathematics/middle-school/q5tdbjcytqej2hfbwsh94etjvna1ij417d.png)
Calculate the difference
![2x = - 5](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qywr2y3lpor9t9hd0cjy1nu6f1rke2qr3j.png)
Divide both sides of the equation by 2
![(2x)/(2) = ( - 5)/(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/k3sg0db6fr6j0u4hi19xcn48qacfrbybza.png)
Calculate
![x 1= - (5)/(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/kt3mxrst67l4lv150mqa69915rzcx339hs.png)
Again,
![3x - 4 = 0](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zp2p548vl4hzea53esmmgsicmitftle5o4.png)
Move constant to RHS and change its sign
![3x = 0 + 4](https://img.qammunity.org/2021/formulas/mathematics/middle-school/w4q6tdd5ekvyafdnxpe455mlj1qsagmat2.png)
Calculate the sum
![3x = 4](https://img.qammunity.org/2021/formulas/mathematics/middle-school/7ks5p4ikbx046kg26jpququz67ql8bpk3p.png)
divide both sides of the equation by 3
![(3x)/(3) = (4)/(3)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/zndau6jgyas42wl0vj1bejtse7u5c6jy4a.png)
Calculate
![x 2= (4)/(3)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/xylrk7k0f9llz2sl61drnlozwtgci670fo.png)
Hope this helps..
Best regards!!