(8x-5)(2x+15)=180

Solution for (8x-5)(2x+15)=180 equation:

(8x-5)(2x+15)=180

We move all terms to the left:

(8x-5)(2x+15)-(180)=0

We multiply parentheses ..

(+16x^2+120x-10x-75)-180=0

We get rid of parentheses

16x^2+120x-10x-75-180=0

We add all the numbers together, and all the variables

16x^2+110x-255=0

a = 16; b = 110; c = -255;
Δ = b2-4ac
Δ = 1102-4·16·(-255)
Δ = 28420
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:

$\sqrt{\Delta}=\sqrt{28420}=\sqrt{196*145}=\sqrt{196}*\sqrt{145}=14\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-14\sqrt{145}}{2*16}=\frac{-110-14\sqrt{145}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+14\sqrt{145}}{2*16}=\frac{-110+14\sqrt{145}}{32}
$