(7x-12)(6x+5)=0

Solution for (7x-12)(6x+5)=0 equation:

(7x-12)(6x+5)=0

We multiply parentheses ..

(+42x^2+35x-72x-60)=0

We get rid of parentheses

42x^2+35x-72x-60=0

We add all the numbers together, and all the variables

42x^2-37x-60=0

a = 42; b = -37; c = -60;
Δ = b2-4ac
Δ = -372-4·42·(-60)
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-107}{2*42}=\frac{-70}{84}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+107}{2*42}=\frac{144}{84}
=1+5/7
$