(12x+1)(5x-3)=117

Solution for (12x+1)(5x-3)=117 equation:

(12x+1)(5x-3)=117

We move all terms to the left:

(12x+1)(5x-3)-(117)=0

We multiply parentheses ..

(+60x^2-36x+5x-3)-117=0

We get rid of parentheses

60x^2-36x+5x-3-117=0

We add all the numbers together, and all the variables

60x^2-31x-120=0

a = 60; b = -31; c = -120;
Δ = b2-4ac
Δ = -312-4·60·(-120)
Δ = 29761
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{-(-31)-\sqrt{29761}}{2*60}=\frac{31-\sqrt{29761}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{29761}}{2*60}=\frac{31+\sqrt{29761}}{120}
$