5s=-8s2+3

Solution for 5s=-8s2+3 equation:

5s=-8s^2+3

We move all terms to the left:

5s-(-8s^2+3)=0

We get rid of parentheses

8s^2+5s-3=0

a = 8; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·8·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*8}=\frac{-16}{16}
=-1
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*8}=\frac{6}{16}
=3/8
$