8(s^2)-4s+12=180

Solution for 8(s^2)-4s+12=180 equation:

8(s^2)-4s+12=180

We move all terms to the left:

8(s^2)-4s+12-(180)=0

We add all the numbers together, and all the variables

8s^2-4s-168=0

a = 8; b = -4; c = -168;
Δ = b2-4ac
Δ = -42-4·8·(-168)
Δ = 5392
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:

$\sqrt{\Delta}=\sqrt{5392}=\sqrt{16*337}=\sqrt{16}*\sqrt{337}=4\sqrt{337}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{337}}{2*8}=\frac{4-4\sqrt{337}}{16}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{337}}{2*8}=\frac{4+4\sqrt{337}}{16}
$