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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

63x^2+46x-225=0

a = 63; b = 46; c = -225;
Δ = b2-4ac
Δ = 462-4·63·(-225)
Δ = 58816
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:

$\sqrt{\Delta}=\sqrt{58816}=\sqrt{64*919}=\sqrt{64}*\sqrt{919}=8\sqrt{919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-8\sqrt{919}}{2*63}=\frac{-46-8\sqrt{919}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+8\sqrt{919}}{2*63}=\frac{-46+8\sqrt{919}}{126}
$