72=(3x-1)(2x+2)

Solution for 72=(3x-1)(2x+2) equation:

72=(3x-1)(2x+2)

We move all terms to the left:

72-((3x-1)(2x+2))=0

We multiply parentheses ..

-((+6x^2+6x-2x-2))+72=0


We calculate terms in parentheses: -((+6x^2+6x-2x-2)), so:

(+6x^2+6x-2x-2)

We get rid of parentheses

6x^2+6x-2x-2

We add all the numbers together, and all the variables

6x^2+4x-2

Back to the equation:

-(6x^2+4x-2)


We get rid of parentheses

-6x^2-4x+2+72=0

We add all the numbers together, and all the variables

-6x^2-4x+74=0

a = -6; b = -4; c = +74;
Δ = b2-4ac
Δ = -42-4·(-6)·74
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16\sqrt{7}}{2*-6}=\frac{4-16\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16\sqrt{7}}{2*-6}=\frac{4+16\sqrt{7}}{-12}
$