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-6x^2+195=15
We move all terms to the left:
-6x^2+195-(15)=0
We add all the numbers together, and all the variables
-6x^2+180=0
a = -6; b = 0; c = +180;
Δ = b2-4ac
Δ = 02-4·(-6)·180
Δ = 4320
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*-6}=\frac{0-12\sqrt{30}}{-12} =-\frac{12\sqrt{30}}{-12} =-\frac{\sqrt{30}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*-6}=\frac{0+12\sqrt{30}}{-12} =\frac{12\sqrt{30}}{-12} =\frac{\sqrt{30}}{-1} $
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