0=x^2-31x-450

Solution for 0=x^2-31x-450 equation:

0=x^2-31x-450

We move all terms to the left:

0-(x^2-31x-450)=0

We add all the numbers together, and all the variables

-(x^2-31x-450)=0

We get rid of parentheses

-x^2+31x+450=0

We add all the numbers together, and all the variables

-1x^2+31x+450=0

a = -1; b = 31; c = +450;
Δ = b2-4ac
Δ = 312-4·(-1)·450
Δ = 2761
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{-(31)-\sqrt{2761}}{2*-1}=\frac{-31-\sqrt{2761}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{2761}}{2*-1}=\frac{-31+\sqrt{2761}}{-2}
$