(3s-4)(3s+6)=s

Solution for (3s-4)(3s+6)=s equation:

(3s-4)(3s+6)=s

We move all terms to the left:

(3s-4)(3s+6)-(s)=0

We add all the numbers together, and all the variables

-1s+(3s-4)(3s+6)=0

We multiply parentheses ..

(+9s^2+18s-12s-24)-1s=0

We get rid of parentheses

9s^2+18s-12s-1s-24=0

We add all the numbers together, and all the variables

9s^2+5s-24=0

a = 9; b = 5; c = -24;
Δ = b2-4ac
Δ = 52-4·9·(-24)
Δ = 889
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{889}}{2*9}=\frac{-5-\sqrt{889}}{18}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{889}}{2*9}=\frac{-5+\sqrt{889}}{18}
$