72=x(x+1)

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

72=x(x+1)

We move all terms to the left:

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


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

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+72=0

We add all the numbers together, and all the variables

-1x^2-1x+72=0

a = -1; b = -1; c = +72;
Δ = b2-4ac
Δ = -12-4·(-1)·72
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*-1}=\frac{18}{-2}
=-9
$