(4x+13)(3x+1)=180

Solution for (4x+13)(3x+1)=180 equation:

(4x+13)(3x+1)=180

We move all terms to the left:

(4x+13)(3x+1)-(180)=0

We multiply parentheses ..

(+12x^2+4x+39x+13)-180=0

We get rid of parentheses

12x^2+4x+39x+13-180=0

We add all the numbers together, and all the variables

12x^2+43x-167=0

a = 12; b = 43; c = -167;
Δ = b2-4ac
Δ = 432-4·12·(-167)
Δ = 9865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-\sqrt{9865}}{2*12}=\frac{-43-\sqrt{9865}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{9865}}{2*12}=\frac{-43+\sqrt{9865}}{24}
$