(x-6)(2x-6)=3x^2

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Solution for (x-6)(2x-6)=3x^2 equation:



(x-6)(2x-6)=3x^2
We move all terms to the left:
(x-6)(2x-6)-(3x^2)=0
determiningTheFunctionDomain -3x^2+(x-6)(2x-6)=0
We multiply parentheses ..
-3x^2+(+2x^2-6x-12x+36)=0
We get rid of parentheses
-3x^2+2x^2-6x-12x+36=0
We add all the numbers together, and all the variables
-1x^2-18x+36=0
a = -1; b = -18; c = +36;
Δ = b2-4ac
Δ = -182-4·(-1)·36
Δ = 468
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:
$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{13}}{2*-1}=\frac{18-6\sqrt{13}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{13}}{2*-1}=\frac{18+6\sqrt{13}}{-2} $

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