2x(x-4)-(2x+3)(x-4)=4x(2x-3)-8(1-x)2

Solution for 2x(x-4)-(2x+3)(x-4)=4x(2x-3)-8(1-x)2 equation:

2x(x-4)-(2x+3)(x-4)=4x(2x-3)-8(1-x)2

We move all terms to the left:

2x(x-4)-(2x+3)(x-4)-(4x(2x-3)-8(1-x)2)=0

We add all the numbers together, and all the variables

2x(x-4)-(2x+3)(x-4)-(4x(2x-3)-8(-1x+1)2)=0

We multiply parentheses

2x^2-8x-(2x+3)(x-4)-(4x(2x-3)-8(-1x+1)2)=0

We multiply parentheses ..

2x^2-(+2x^2-8x+3x-12)-8x-(4x(2x-3)-8(-1x+1)2)=0


We calculate terms in parentheses: -(4x(2x-3)-8(-1x+1)2), so:

4x(2x-3)-8(-1x+1)2

We multiply parentheses

8x^2-12x+16x-16

We add all the numbers together, and all the variables

8x^2+4x-16

Back to the equation:

-(8x^2+4x-16)


We get rid of parentheses

2x^2-2x^2-8x^2+8x-3x-8x-4x+12+16=0

We add all the numbers together, and all the variables

-8x^2-7x+28=0

a = -8; b = -7; c = +28;
Δ = b2-4ac
Δ = -72-4·(-8)·28
Δ = 945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{105}}{2*-8}=\frac{7-3\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{105}}{2*-8}=\frac{7+3\sqrt{105}}{-16}
$