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3x^2-2x-117=2x^2-2x
We move all terms to the left:
3x^2-2x-117-(2x^2-2x)=0
We get rid of parentheses
3x^2-2x^2-2x+2x-117=0
We add all the numbers together, and all the variables
x^2-117=0
a = 1; b = 0; c = -117;
Δ = b2-4ac
Δ = 02-4·1·(-117)
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{-(0)-6\sqrt{13}}{2*1}=\frac{0-6\sqrt{13}}{2} =-\frac{6\sqrt{13}}{2} =-3\sqrt{13} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{13}}{2*1}=\frac{0+6\sqrt{13}}{2} =\frac{6\sqrt{13}}{2} =3\sqrt{13} $
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