(12x+2)(13x+19)=121

Solution for (12x+2)(13x+19)=121 equation:

(12x+2)(13x+19)=121

We move all terms to the left:

(12x+2)(13x+19)-(121)=0

We multiply parentheses ..

(+156x^2+228x+26x+38)-121=0

We get rid of parentheses

156x^2+228x+26x+38-121=0

We add all the numbers together, and all the variables

156x^2+254x-83=0

a = 156; b = 254; c = -83;
Δ = b2-4ac
Δ = 2542-4·156·(-83)
Δ = 116308
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:

$\sqrt{\Delta}=\sqrt{116308}=\sqrt{4*29077}=\sqrt{4}*\sqrt{29077}=2\sqrt{29077}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(254)-2\sqrt{29077}}{2*156}=\frac{-254-2\sqrt{29077}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(254)+2\sqrt{29077}}{2*156}=\frac{-254+2\sqrt{29077}}{312}
$