x^2+3=8x-x^2

Solution for x^2+3=8x-x^2 equation:

x^2+3=8x-x^2

We move all terms to the left:

x^2+3-(8x-x^2)=0

We get rid of parentheses

x^2+x^2-8x+3=0

We add all the numbers together, and all the variables

2x^2-8x+3=0

a = 2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·2·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{10}}{2*2}=\frac{8-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*2}=\frac{8+2\sqrt{10}}{4}
$