(3s-2)(4s-6)=180

Solution for (3s-2)(4s-6)=180 equation:

(3s-2)(4s-6)=180

We move all terms to the left:

(3s-2)(4s-6)-(180)=0

We multiply parentheses ..

(+12s^2-18s-8s+12)-180=0

We get rid of parentheses

12s^2-18s-8s+12-180=0

We add all the numbers together, and all the variables

12s^2-26s-168=0

a = 12; b = -26; c = -168;
Δ = b2-4ac
Δ = -262-4·12·(-168)
Δ = 8740
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:

$\sqrt{\Delta}=\sqrt{8740}=\sqrt{4*2185}=\sqrt{4}*\sqrt{2185}=2\sqrt{2185}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{2185}}{2*12}=\frac{26-2\sqrt{2185}}{24}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{2185}}{2*12}=\frac{26+2\sqrt{2185}}{24}
$