(2x-7)(2x-5)13=180

Solution for (2x-7)(2x-5)13=180 equation:

(2x-7)(2x-5)13=180

We move all terms to the left:

(2x-7)(2x-5)13-(180)=0

We multiply parentheses ..

(+4x^2-10x-14x+35)13-180=0

We multiply parentheses

52x^2-130x-182x+455-180=0

We add all the numbers together, and all the variables

52x^2-312x+275=0

a = 52; b = -312; c = +275;
Δ = b2-4ac
Δ = -3122-4·52·275
Δ = 40144
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:

$\sqrt{\Delta}=\sqrt{40144}=\sqrt{16*2509}=\sqrt{16}*\sqrt{2509}=4\sqrt{2509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-4\sqrt{2509}}{2*52}=\frac{312-4\sqrt{2509}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+4\sqrt{2509}}{2*52}=\frac{312+4\sqrt{2509}}{104}
$