X^2-6x+9=x+5

Solution for X^2-6x+9=x+5 equation:

X^2-6X+9=X+5

We move all terms to the left:

X^2-6X+9-(X+5)=0

We get rid of parentheses

X^2-6X-X-5+9=0

We add all the numbers together, and all the variables

X^2-7X+4=0

a = 1; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·1·4
Δ = 33
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{-(-7)-\sqrt{33}}{2*1}=\frac{7-\sqrt{33}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*1}=\frac{7+\sqrt{33}}{2}
$