(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+116x-135=0

a = 63; b = 116; c = -135;
Δ = b2-4ac
Δ = 1162-4·63·(-135)
Δ = 47476
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:

$\sqrt{\Delta}=\sqrt{47476}=\sqrt{4*11869}=\sqrt{4}*\sqrt{11869}=2\sqrt{11869}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-2\sqrt{11869}}{2*63}=\frac{-116-2\sqrt{11869}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+2\sqrt{11869}}{2*63}=\frac{-116+2\sqrt{11869}}{126}
$