s^2+5s=100

Solution for s^2+5s=100 equation:

s^2+5s=100

We move all terms to the left:

s^2+5s-(100)=0

a = 1; b = 5; c = -100;
Δ = b2-4ac
Δ = 52-4·1·(-100)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{17}}{2*1}=\frac{-5-5\sqrt{17}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{17}}{2*1}=\frac{-5+5\sqrt{17}}{2}
$