Question

How do you solve 4x squared - 12x = 7 (ALGEBRAICALLY)

Answer 1

`\rm 4x^2-12x=7 \\ \\ 4x^2-12x-7=0 \\ \\ 4x^2+2x-14x-7=0 \\ \\ 2x(2x+1)-7(2x+1)=0 \\ \\ (2x+1)(2x-7)=0 \\ \\ I.~2x+1=0 \longrightarrow \bold{x=-\frac12} \\ ~~~~~~~~~~~~~~or \\ \\ II.~2x-7=0 \longrightarrow \bold{x=\frac72}`

Answer 2

`4x^2-12x=7 \\ 4x^2-12x-7=0 \\ \\ a=4 \\ b=-12 \\ c=-7 \\ b^2-4ac=(-12)^2-4 * 4 * (-7)=144+112=256 \\ \\ x=(-b \pm √(b^2-4ac))/(2a)=(-(-12) \pm √(256))/(2 * 4)=(12 \pm 16)/(2 * 4)=(4(3 \pm 4))/(2 * 4)=(3 \pm 4)/(2) \\ x=(3-4)/(2) \ \lor \ x=(3+4)/(2) \\ x=-(1)/(2) \ \lor \ x=(7)/(2) \\ \\ \boxed{x=-(1)/(2) \hbox{ or } x=(7)/(2)}`