0=x^2-9x-972

Solution for 0=x^2-9x-972 equation:

0=x^2-9x-972

We move all terms to the left:

0-(x^2-9x-972)=0

We add all the numbers together, and all the variables

-(x^2-9x-972)=0

We get rid of parentheses

-x^2+9x+972=0

We add all the numbers together, and all the variables

-1x^2+9x+972=0

a = -1; b = 9; c = +972;
Δ = b2-4ac
Δ = 92-4·(-1)·972
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-63}{2*-1}=\frac{-72}{-2}
=+36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+63}{2*-1}=\frac{54}{-2}
=-27
$