x^2-18x+6=150

Solution for x^2-18x+6=150 equation:

x^2-18x+6=150

We move all terms to the left:

x^2-18x+6-(150)=0

We add all the numbers together, and all the variables

x^2-18x-144=0

a = 1; b = -18; c = -144;
Δ = b2-4ac
Δ = -182-4·1·(-144)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*1}=\frac{48}{2}
=24
$