-12x-(8x+4)+10x=-2x(x+1)

Solution for -12x-(8x+4)+10x=-2x(x+1) equation:

-12x-(8x+4)+10x=-2x(x+1)

We move all terms to the left:

-12x-(8x+4)+10x-(-2x(x+1))=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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


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

-2x(x+1)

We multiply parentheses

-2x^2-2x

Back to the equation:

-(-2x^2-2x)


We add all the numbers together, and all the variables

-(-2x^2-2x)-10x-4=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-8x-4=0

a = 2; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·2·(-4)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*2}=\frac{8-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*2}=\frac{8+4\sqrt{6}}{4}
$