(13x+9)(5x+9)=180

Solution for (13x+9)(5x+9)=180 equation:

(13x+9)(5x+9)=180

We move all terms to the left:

(13x+9)(5x+9)-(180)=0

We multiply parentheses ..

(+65x^2+117x+45x+81)-180=0

We get rid of parentheses

65x^2+117x+45x+81-180=0

We add all the numbers together, and all the variables

65x^2+162x-99=0

a = 65; b = 162; c = -99;
Δ = b2-4ac
Δ = 1622-4·65·(-99)
Δ = 51984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51984}=228$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-228}{2*65}=\frac{-390}{130}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+228}{2*65}=\frac{66}{130}
=33/65
$