-10s(s+2)=-53

Solution for -10s(s+2)=-53 equation:

-10s(s+2)=-53

We move all terms to the left:

-10s(s+2)-(-53)=0

We add all the numbers together, and all the variables

-10s(s+2)+53=0

We multiply parentheses

-10s^2-20s+53=0

a = -10; b = -20; c = +53;
Δ = b2-4ac
Δ = -202-4·(-10)·53
Δ = 2520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{70}}{2*-10}=\frac{20-6\sqrt{70}}{-20}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{70}}{2*-10}=\frac{20+6\sqrt{70}}{-20}
$