0=180s^2-186s-360

Solution for 0=180s^2-186s-360 equation:

0=180s^2-186s-360

We move all terms to the left:

0-(180s^2-186s-360)=0

We add all the numbers together, and all the variables

-(180s^2-186s-360)=0

We get rid of parentheses

-180s^2+186s+360=0

a = -180; b = 186; c = +360;
Δ = b2-4ac
Δ = 1862-4·(-180)·360
Δ = 293796
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:

$\sqrt{\Delta}=\sqrt{293796}=\sqrt{36*8161}=\sqrt{36}*\sqrt{8161}=6\sqrt{8161}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(186)-6\sqrt{8161}}{2*-180}=\frac{-186-6\sqrt{8161}}{-360}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(186)+6\sqrt{8161}}{2*-180}=\frac{-186+6\sqrt{8161}}{-360}
$