(10x-27)(2x+29)=180

Solution for (10x-27)(2x+29)=180 equation:

(10x-27)(2x+29)=180

We move all terms to the left:

(10x-27)(2x+29)-(180)=0

We multiply parentheses ..

(+20x^2+290x-54x-783)-180=0

We get rid of parentheses

20x^2+290x-54x-783-180=0

We add all the numbers together, and all the variables

20x^2+236x-963=0

a = 20; b = 236; c = -963;
Δ = b2-4ac
Δ = 2362-4·20·(-963)
Δ = 132736
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:

$\sqrt{\Delta}=\sqrt{132736}=\sqrt{64*2074}=\sqrt{64}*\sqrt{2074}=8\sqrt{2074}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(236)-8\sqrt{2074}}{2*20}=\frac{-236-8\sqrt{2074}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(236)+8\sqrt{2074}}{2*20}=\frac{-236+8\sqrt{2074}}{40}
$