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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+10x-5=0

a = -4; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·(-4)·(-5)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{5}}{2*-4}=\frac{-10-2\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{5}}{2*-4}=\frac{-10+2\sqrt{5}}{-8}
$