-6x-13=-x2+14

Solution for -6x-13=-x2+14 equation:

-6x-13=-x2+14

We move all terms to the left:

-6x-13-(-x2+14)=0

We add all the numbers together, and all the variables

-(-1x^2+14)-6x-13=0

We get rid of parentheses

1x^2-6x-14-13=0

We add all the numbers together, and all the variables

x^2-6x-27=0

a = 1; b = -6; c = -27;
Δ = b2-4ac
Δ = -62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*1}=\frac{18}{2}
=9
$