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-6x^2=-414
We move all terms to the left:
-6x^2-(-414)=0
We add all the numbers together, and all the variables
-6x^2+414=0
a = -6; b = 0; c = +414;
Δ = b2-4ac
Δ = 02-4·(-6)·414
Δ = 9936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9936}=\sqrt{144*69}=\sqrt{144}*\sqrt{69}=12\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{69}}{2*-6}=\frac{0-12\sqrt{69}}{-12} =-\frac{12\sqrt{69}}{-12} =-\frac{\sqrt{69}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{69}}{2*-6}=\frac{0+12\sqrt{69}}{-12} =\frac{12\sqrt{69}}{-12} =\frac{\sqrt{69}}{-1} $
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