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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+35x-193=0

a = 12; b = 35; c = -193;
Δ = b2-4ac
Δ = 352-4·12·(-193)
Δ = 10489
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{-(35)-\sqrt{10489}}{2*12}=\frac{-35-\sqrt{10489}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{10489}}{2*12}=\frac{-35+\sqrt{10489}}{24}
$