(7x-5)(9x-7)=180

Solution for (7x-5)(9x-7)=180 equation:

(7x-5)(9x-7)=180

We move all terms to the left:

(7x-5)(9x-7)-(180)=0

We multiply parentheses ..

(+63x^2-49x-45x+35)-180=0

We get rid of parentheses

63x^2-49x-45x+35-180=0

We add all the numbers together, and all the variables

63x^2-94x-145=0

a = 63; b = -94; c = -145;
Δ = b2-4ac
Δ = -942-4·63·(-145)
Δ = 45376
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:

$\sqrt{\Delta}=\sqrt{45376}=\sqrt{64*709}=\sqrt{64}*\sqrt{709}=8\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-94)-8\sqrt{709}}{2*63}=\frac{94-8\sqrt{709}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94)+8\sqrt{709}}{2*63}=\frac{94+8\sqrt{709}}{126}
$