5s(3+s)=150

Solution for 5s(3+s)=150 equation:

5s(3+s)=150

We move all terms to the left:

5s(3+s)-(150)=0

We add all the numbers together, and all the variables

5s(s+3)-150=0

We multiply parentheses

5s^2+15s-150=0

a = 5; b = 15; c = -150;
Δ = b2-4ac
Δ = 152-4·5·(-150)
Δ = 3225
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:

$\sqrt{\Delta}=\sqrt{3225}=\sqrt{25*129}=\sqrt{25}*\sqrt{129}=5\sqrt{129}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{129}}{2*5}=\frac{-15-5\sqrt{129}}{10}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{129}}{2*5}=\frac{-15+5\sqrt{129}}{10}
$