x^2-6x+18=3x^2-x+6

Solution for x^2-6x+18=3x^2-x+6 equation:

x^2-6x+18=3x^2-x+6

We move all terms to the left:

x^2-6x+18-(3x^2-x+6)=0

We get rid of parentheses

x^2-3x^2-6x+x-6+18=0

We add all the numbers together, and all the variables

-2x^2-5x+12=0

a = -2; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-2)·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-2}=\frac{16}{-4}
=-4
$