X2-4x-13=6x-2

Solution for X2-4x-13=6x-2 equation:

X2-4X-13=6X-2

We move all terms to the left:

X2-4X-13-(6X-2)=0

We add all the numbers together, and all the variables

X^2-4X-(6X-2)-13=0

We get rid of parentheses

X^2-4X-6X+2-13=0

We add all the numbers together, and all the variables

X^2-10X-11=0

a = 1; b = -10; c = -11;
Δ = b2-4ac
Δ = -102-4·1·(-11)
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{-(-10)-12}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+12}{2*1}=\frac{22}{2}
=11
$