X^2-15x+13=-6x

Solution for X^2-15x+13=-6x equation:

X^2-15X+13=-6X

We move all terms to the left:

X^2-15X+13-(-6X)=0

We get rid of parentheses

X^2-15X+6X+13=0

We add all the numbers together, and all the variables

X^2-9X+13=0

a = 1; b = -9; c = +13;
Δ = b2-4ac
Δ = -92-4·1·13
Δ = 29
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{-(-9)-\sqrt{29}}{2*1}=\frac{9-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{29}}{2*1}=\frac{9+\sqrt{29}}{2}
$