x^2-3x+2=12^2

Solution for x^2-3x+2=12^2 equation:

x^2-3x+2=12^2

We move all terms to the left:

x^2-3x+2-(12^2)=0

We add all the numbers together, and all the variables

x^2-3x-142=0

a = 1; b = -3; c = -142;
Δ = b2-4ac
Δ = -32-4·1·(-142)
Δ = 577
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{-(-3)-\sqrt{577}}{2*1}=\frac{3-\sqrt{577}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{577}}{2*1}=\frac{3+\sqrt{577}}{2}
$