(8x-27)(7x-4)=180

Solution for (8x-27)(7x-4)=180 equation:

(8x-27)(7x-4)=180

We move all terms to the left:

(8x-27)(7x-4)-(180)=0

We multiply parentheses ..

(+56x^2-32x-189x+108)-180=0

We get rid of parentheses

56x^2-32x-189x+108-180=0

We add all the numbers together, and all the variables

56x^2-221x-72=0

a = 56; b = -221; c = -72;
Δ = b2-4ac
Δ = -2212-4·56·(-72)
Δ = 64969
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{-(-221)-\sqrt{64969}}{2*56}=\frac{221-\sqrt{64969}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-221)+\sqrt{64969}}{2*56}=\frac{221+\sqrt{64969}}{112}
$