x2-6x+13=3x-5

Solution for x2-6x+13=3x-5 equation:

x2-6x+13=3x-5

We move all terms to the left:

x2-6x+13-(3x-5)=0

We add all the numbers together, and all the variables

x^2-6x-(3x-5)+13=0

We get rid of parentheses

x^2-6x-3x+5+13=0

We add all the numbers together, and all the variables

x^2-9x+18=0

a = 1; b = -9; c = +18;
Δ = b2-4ac
Δ = -92-4·1·18
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*1}=\frac{12}{2}
=6
$