0=12x^2+5x-72

Solution for 0=12x^2+5x-72 equation:

0=12x^2+5x-72

We move all terms to the left:

0-(12x^2+5x-72)=0

We add all the numbers together, and all the variables

-(12x^2+5x-72)=0

We get rid of parentheses

-12x^2-5x+72=0

a = -12; b = -5; c = +72;
Δ = b2-4ac
Δ = -52-4·(-12)·72
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-59}{2*-12}=\frac{-54}{-24}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+59}{2*-12}=\frac{64}{-24}
=-2+2/3
$