(13x+)(9x+3)=180

Solution for (13x+)(9x+3)=180 equation:

(13x+)(9x+3)=180

We move all terms to the left:

(13x+)(9x+3)-(180)=0

We add all the numbers together, and all the variables

(+13x)(9x+3)-180=0

We multiply parentheses ..

(+117x^2+39x)-180=0

We get rid of parentheses

117x^2+39x-180=0

a = 117; b = 39; c = -180;
Δ = b2-4ac
Δ = 392-4·117·(-180)
Δ = 85761
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:

$\sqrt{\Delta}=\sqrt{85761}=\sqrt{9*9529}=\sqrt{9}*\sqrt{9529}=3\sqrt{9529}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{9529}}{2*117}=\frac{-39-3\sqrt{9529}}{234}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{9529}}{2*117}=\frac{-39+3\sqrt{9529}}{234}
$