X2-6x+5=3x-13

Solution for X2-6x+5=3x-13 equation:

X2-6X+5=3X-13

We move all terms to the left:

X2-6X+5-(3X-13)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

X^2-6X-3X+13+5=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
$