x^2-x+13=-9x-2

Solution for x^2-x+13=-9x-2 equation:

x^2-x+13=-9x-2

We move all terms to the left:

x^2-x+13-(-9x-2)=0

We add all the numbers together, and all the variables

x^2-1x-(-9x-2)+13=0

We get rid of parentheses

x^2-1x+9x+2+13=0

We add all the numbers together, and all the variables

x^2+8x+15=0

a = 1; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*1}=\frac{-6}{2}
=-3
$