2x(4-4x)+7=2x-5

Solution for 2x(4-4x)+7=2x-5 equation:

2x(4-4x)+7=2x-5

We move all terms to the left:

2x(4-4x)+7-(2x-5)=0

We add all the numbers together, and all the variables

2x(-4x+4)-(2x-5)+7=0

We multiply parentheses

-8x^2+8x-(2x-5)+7=0

We get rid of parentheses

-8x^2+8x-2x+5+7=0

We add all the numbers together, and all the variables

-8x^2+6x+12=0

a = -8; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-8)·12
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{105}}{2*-8}=\frac{-6-2\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{105}}{2*-8}=\frac{-6+2\sqrt{105}}{-16}
$