4x^2-13=8x+x^2

Solution for 4x^2-13=8x+x^2 equation:

4x^2-13=8x+x^2

We move all terms to the left:

4x^2-13-(8x+x^2)=0

We get rid of parentheses

4x^2-x^2-8x-13=0

We add all the numbers together, and all the variables

3x^2-8x-13=0

a = 3; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·3·(-13)
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{55}}{2*3}=\frac{8-2\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{55}}{2*3}=\frac{8+2\sqrt{55}}{6}
$