(12x+6)(-1+13x)=180

Solution for (12x+6)(-1+13x)=180 equation:

(12x+6)(-1+13x)=180

We move all terms to the left:

(12x+6)(-1+13x)-(180)=0

We add all the numbers together, and all the variables

(12x+6)(13x-1)-180=0

We multiply parentheses ..

(+156x^2-12x+78x-6)-180=0

We get rid of parentheses

156x^2-12x+78x-6-180=0

We add all the numbers together, and all the variables

156x^2+66x-186=0

a = 156; b = 66; c = -186;
Δ = b2-4ac
Δ = 662-4·156·(-186)
Δ = 120420
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:

$\sqrt{\Delta}=\sqrt{120420}=\sqrt{36*3345}=\sqrt{36}*\sqrt{3345}=6\sqrt{3345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{3345}}{2*156}=\frac{-66-6\sqrt{3345}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{3345}}{2*156}=\frac{-66+6\sqrt{3345}}{312}
$