-10x(x+1)=0

Solution for -10x(x+1)=0 equation:

-10x(x+1)=0

We multiply parentheses

-10x^2-10x=0

a = -10; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-10)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-10}=\frac{20}{-20}
=-1
$