X^2-6x+5=5-x^2

Solution for X^2-6x+5=5-x^2 equation:

X^2-6X+5=5-X^2

We move all terms to the left:

X^2-6X+5-(5-X^2)=0

We get rid of parentheses

X^2+X^2-6X-5+5=0

We add all the numbers together, and all the variables

2X^2-6X=0

a = 2; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·2·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*2}=\frac{12}{4}
=3
$