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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+35x^2-45x+63x-81)-180=0

We get rid of parentheses

35x^2-45x+63x-81-180=0

We add all the numbers together, and all the variables

35x^2+18x-261=0

a = 35; b = 18; c = -261;
Δ = b2-4ac
Δ = 182-4·35·(-261)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-192}{2*35}=\frac{-210}{70}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+192}{2*35}=\frac{174}{70}
=2+17/35
$