72=18x-(x*x)

Solution for 72=18x-(x*x) equation:

72=18x-(x*x)

We move all terms to the left:

72-(18x-(x*x))=0

We add all the numbers together, and all the variables

-(18x-(+x*x))+72=0


We calculate terms in parentheses: -(18x-(+x*x)), so:

18x-(+x*x)

We get rid of parentheses

18x-x*x

Wy multiply elements

-1x^2+18x

Back to the equation:

-(-1x^2+18x)


We get rid of parentheses

1x^2-18x+72=0

We add all the numbers together, and all the variables

x^2-18x+72=0

a = 1; b = -18; c = +72;
Δ = b2-4ac
Δ = -182-4·1·72
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*1}=\frac{24}{2}
=12
$