10s(s-7)=-116

Solution for 10s(s-7)=-116 equation:

10s(s-7)=-116

We move all terms to the left:

10s(s-7)-(-116)=0

We add all the numbers together, and all the variables

10s(s-7)+116=0

We multiply parentheses

10s^2-70s+116=0

a = 10; b = -70; c = +116;
Δ = b2-4ac
Δ = -702-4·10·116
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{65}}{2*10}=\frac{70-2\sqrt{65}}{20}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{65}}{2*10}=\frac{70+2\sqrt{65}}{20}
$