(2x-11)(x+35)=180

Solution for (2x-11)(x+35)=180 equation:

(2x-11)(x+35)=180

We move all terms to the left:

(2x-11)(x+35)-(180)=0

We multiply parentheses ..

(+2x^2+70x-11x-385)-180=0

We get rid of parentheses

2x^2+70x-11x-385-180=0

We add all the numbers together, and all the variables

2x^2+59x-565=0

a = 2; b = 59; c = -565;
Δ = b2-4ac
Δ = 592-4·2·(-565)
Δ = 8001
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:

$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-3\sqrt{889}}{2*2}=\frac{-59-3\sqrt{889}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+3\sqrt{889}}{2*2}=\frac{-59+3\sqrt{889}}{4}
$