72=6x(x+1)

Solution for 72=6x(x+1) equation:

72=6x(x+1)

We move all terms to the left:

72-(6x(x+1))=0


We calculate terms in parentheses: -(6x(x+1)), so:

6x(x+1)

We multiply parentheses

6x^2+6x

Back to the equation:

-(6x^2+6x)


We get rid of parentheses

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

a = -6; b = -6; c = +72;
Δ = b2-4ac
Δ = -62-4·(-6)·72
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*-6}=\frac{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*-6}=\frac{48}{-12}
=-4
$