Question

How to solve this quadratic expression

`2x(x - 3) = 3 - 4x`
​

Answer 1

Let's simplify the given expression at first!

`\: \:\:\:\: \longrightarrow\sf {2x(x - 3) = 3 - 4x}\\`

`\: \:\:\:\: \longrightarrow\sf {2x^2 -6x = 3 -4x}\\`

`\: \:\:\:\: \longrightarrow\sf {2x^2 -6x+4x-3=0}\\`

And here it is -

`\: \:\:\:\: \small \underline{ \boxed{ \sf{ \pmb{ 2x^2 -2x -3 =0}}}}\\`

Where-

• a =2
• b=-2
• c =-3

To find the Discriminant of this equation is given by -

`\longrightarrow\underline\purple{\boxed{\pmb{D = b^2-4ac}}}`

`\: \:\:\:\: \longrightarrow\sf { D = (-2)^2 - 4* 2* -3}\\`

`\: \:\:\:\: \longrightarrow\sf { D = 4 + 24}\\`

`\: \:\:\:\: \longrightarrow\sf { D = 28}\\`

Since, D>0 hence, this equation has two distinct real roots.

Formula to be applied now is as follows-

`\: \:\:\:\: \longrightarrow\underline\purple{\boxed{\pmb{ x = (-b±√D)/(2a)}}}`

`\: \:\:\:\: \longrightarrow\sf { x = (-(-2)± √(28))/(2 * 2)}\\`

`\: \:\:\:\: \longrightarrow\sf {x = (2± √(4 * 7))/(2 * 2)}\\`

`\: \:\:\:\: \longrightarrow\sf {x = (2± 2* √(7 ))/(2 * 2)}\\`

`\: \:\:\:\: \longrightarrow\sf {x = (2 (1± √(7)) )/(2 * 2)}\\`

`\: \:\:\:\: \longrightarrow\sf {x = \frac{\cancel{2 }(1± √(7)) }{\cancel{2 }* 2}}\\`

`\: \:\:\:\: \longrightarrow \boxed{ \tt{ \pmb{ \red{x = ( 1± √(7) )/( 2)}}}}\\`

`\\ \therefore \underline{ \cal{ \pmb{The \:value \: of \:x \: is \: \frak{\purple{ ( 1± √(7) )/( 2) \: }. }}}}\\`