(8x-31)(6x+3)=180

Solution for (8x-31)(6x+3)=180 equation:

(8x-31)(6x+3)=180

We move all terms to the left:

(8x-31)(6x+3)-(180)=0

We multiply parentheses ..

(+48x^2+24x-186x-93)-180=0

We get rid of parentheses

48x^2+24x-186x-93-180=0

We add all the numbers together, and all the variables

48x^2-162x-273=0

a = 48; b = -162; c = -273;
Δ = b2-4ac
Δ = -1622-4·48·(-273)
Δ = 78660
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:

$\sqrt{\Delta}=\sqrt{78660}=\sqrt{36*2185}=\sqrt{36}*\sqrt{2185}=6\sqrt{2185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-6\sqrt{2185}}{2*48}=\frac{162-6\sqrt{2185}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+6\sqrt{2185}}{2*48}=\frac{162+6\sqrt{2185}}{96}
$