-2x(x+1)2=-10

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

-2x(x+1)2=-10

We move all terms to the left:

-2x(x+1)2-(-10)=0

We add all the numbers together, and all the variables

-2x(x+1)2+10=0

We multiply parentheses

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

a = -4; b = -4; c = +10;
Δ = b2-4ac
Δ = -42-4·(-4)·10
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*-4}=\frac{4-4\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*-4}=\frac{4+4\sqrt{11}}{-8}
$