12-(2x)-10+(-4x)x=-5

Solution for 12-(2x)-10+(-4x)x=-5 equation:

12-(2x)-10+(-4x)x=-5

We move all terms to the left:

12-(2x)-10+(-4x)x-(-5)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2-2x+7=0

a = -4; b = -2; c = +7;
Δ = b2-4ac
Δ = -22-4·(-4)·7
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*-4}=\frac{2-2\sqrt{29}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*-4}=\frac{2+2\sqrt{29}}{-8}
$