(8x-27)(5x+2)=180

Solution for (8x-27)(5x+2)=180 equation:

(8x-27)(5x+2)=180

We move all terms to the left:

(8x-27)(5x+2)-(180)=0

We multiply parentheses ..

(+40x^2+16x-135x-54)-180=0

We get rid of parentheses

40x^2+16x-135x-54-180=0

We add all the numbers together, and all the variables

40x^2-119x-234=0

a = 40; b = -119; c = -234;
Δ = b2-4ac
Δ = -1192-4·40·(-234)
Δ = 51601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-\sqrt{51601}}{2*40}=\frac{119-\sqrt{51601}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{51601}}{2*40}=\frac{119+\sqrt{51601}}{80}
$