-2x(10+5x)+10=2x-118

Solution for -2x(10+5x)+10=2x-118 equation:

-2x(10+5x)+10=2x-118

We move all terms to the left:

-2x(10+5x)+10-(2x-118)=0

We add all the numbers together, and all the variables

-2x(5x+10)-(2x-118)+10=0

We multiply parentheses

-10x^2-20x-(2x-118)+10=0

We get rid of parentheses

-10x^2-20x-2x+118+10=0

We add all the numbers together, and all the variables

-10x^2-22x+128=0

a = -10; b = -22; c = +128;
Δ = b2-4ac
Δ = -222-4·(-10)·128
Δ = 5604
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:

$\sqrt{\Delta}=\sqrt{5604}=\sqrt{4*1401}=\sqrt{4}*\sqrt{1401}=2\sqrt{1401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{1401}}{2*-10}=\frac{22-2\sqrt{1401}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{1401}}{2*-10}=\frac{22+2\sqrt{1401}}{-20}
$