8s^2-13s=-2/3

Solution for 8s^2-13s=-2/3 equation:

8s^2-13s=-2/3

We move all terms to the left:

8s^2-13s-(-2/3)=0

We get rid of parentheses

8s^2-13s+2/3=0

We multiply all the terms by the denominator


8s^2*3-13s*3+2=0

Wy multiply elements

24s^2-39s+2=0

a = 24; b = -39; c = +2;
Δ = b2-4ac
Δ = -392-4·24·2
Δ = 1329
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{-(-39)-\sqrt{1329}}{2*24}=\frac{39-\sqrt{1329}}{48}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1329}}{2*24}=\frac{39+\sqrt{1329}}{48}
$