4s^2=5s+5

Solution for 4s^2=5s+5 equation:

4s^2=5s+5

We move all terms to the left:

4s^2-(5s+5)=0

We get rid of parentheses

4s^2-5s-5=0

a = 4; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·4·(-5)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*4}=\frac{5-\sqrt{105}}{8}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*4}=\frac{5+\sqrt{105}}{8}
$