(3x-12)(2x-7)=5

Solution for (3x-12)(2x-7)=5 equation:

(3x-12)(2x-7)=5

We move all terms to the left:

(3x-12)(2x-7)-(5)=0

We multiply parentheses ..

(+6x^2-21x-24x+84)-5=0

We get rid of parentheses

6x^2-21x-24x+84-5=0

We add all the numbers together, and all the variables

6x^2-45x+79=0

a = 6; b = -45; c = +79;
Δ = b2-4ac
Δ = -452-4·6·79
Δ = 129
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{-(-45)-\sqrt{129}}{2*6}=\frac{45-\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{129}}{2*6}=\frac{45+\sqrt{129}}{12}
$