0=x^2-23x-72

Solution for 0=x^2-23x-72 equation:

0=x^2-23x-72

We move all terms to the left:

0-(x^2-23x-72)=0

We add all the numbers together, and all the variables

-(x^2-23x-72)=0

We get rid of parentheses

-x^2+23x+72=0

We add all the numbers together, and all the variables

-1x^2+23x+72=0

a = -1; b = 23; c = +72;
Δ = b2-4ac
Δ = 232-4·(-1)·72
Δ = 817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{817}}{2*-1}=\frac{-23-\sqrt{817}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{817}}{2*-1}=\frac{-23+\sqrt{817}}{-2}
$