8x(x+31)=180

Solution for 8x(x+31)=180 equation:

8x(x+31)=180

We move all terms to the left:

8x(x+31)-(180)=0

We multiply parentheses

8x^2+248x-180=0

a = 8; b = 248; c = -180;
Δ = b2-4ac
Δ = 2482-4·8·(-180)
Δ = 67264
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:

$\sqrt{\Delta}=\sqrt{67264}=\sqrt{64*1051}=\sqrt{64}*\sqrt{1051}=8\sqrt{1051}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(248)-8\sqrt{1051}}{2*8}=\frac{-248-8\sqrt{1051}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(248)+8\sqrt{1051}}{2*8}=\frac{-248+8\sqrt{1051}}{16}
$