4s(s-30)=5

Solution for 4s(s-30)=5 equation:

4s(s-30)=5

We move all terms to the left:

4s(s-30)-(5)=0

We multiply parentheses

4s^2-120s-5=0

a = 4; b = -120; c = -5;
Δ = b2-4ac
Δ = -1202-4·4·(-5)
Δ = 14480
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:

$\sqrt{\Delta}=\sqrt{14480}=\sqrt{16*905}=\sqrt{16}*\sqrt{905}=4\sqrt{905}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{905}}{2*4}=\frac{120-4\sqrt{905}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{905}}{2*4}=\frac{120+4\sqrt{905}}{8}
$