x2-12x+23=2x2-22x+39

Solution for x2-12x+23=2x2-22x+39 equation:

x2-12x+23=2x^2-22x+39

We move all terms to the left:

x2-12x+23-(2x^2-22x+39)=0

We add all the numbers together, and all the variables

x^2-12x-(2x^2-22x+39)+23=0

We get rid of parentheses

x^2-2x^2-12x+22x-39+23=0

We add all the numbers together, and all the variables

-1x^2+10x-16=0

a = -1; b = 10; c = -16;
Δ = b2-4ac
Δ = 102-4·(-1)·(-16)
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{-(10)-6}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6}{2*-1}=\frac{-4}{-2}
=+2
$