x^2=23-12x

Solution for x^2=23-12x equation:

x^2=23-12x

We move all terms to the left:

x^2-(23-12x)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2+12x-23=0

a = 1; b = 12; c = -23;
Δ = b2-4ac
Δ = 122-4·1·(-23)
Δ = 236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{59}}{2*1}=\frac{-12-2\sqrt{59}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{59}}{2*1}=\frac{-12+2\sqrt{59}}{2}
$