2x(x+1)=72

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

2x(x+1)=72

We move all terms to the left:

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

We multiply parentheses

2x^2+2x-72=0

a = 2; b = 2; c = -72;
Δ = b2-4ac
Δ = 22-4·2·(-72)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{145}}{2*2}=\frac{-2-2\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{145}}{2*2}=\frac{-2+2\sqrt{145}}{4}
$