0=X^2+14x-527

Solution for 0=X^2+14x-527 equation:

0=X^2+14X-527

We move all terms to the left:

0-(X^2+14X-527)=0

We add all the numbers together, and all the variables

-(X^2+14X-527)=0

We get rid of parentheses

-X^2-14X+527=0

We add all the numbers together, and all the variables

-1X^2-14X+527=0

a = -1; b = -14; c = +527;
Δ = b2-4ac
Δ = -142-4·(-1)·527
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-48}{2*-1}=\frac{-34}{-2}
=+17
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+48}{2*-1}=\frac{62}{-2}
=-31
$