8x+2x^2=180

Solution for 8x+2x^2=180 equation:

8x+2x^2=180

We move all terms to the left:

8x+2x^2-(180)=0

a = 2; b = 8; c = -180;
Δ = b2-4ac
Δ = 82-4·2·(-180)
Δ = 1504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{94}}{2*2}=\frac{-8-4\sqrt{94}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{94}}{2*2}=\frac{-8+4\sqrt{94}}{4}
$