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5x^2+12=120
We move all terms to the left:
5x^2+12-(120)=0
We add all the numbers together, and all the variables
5x^2-108=0
a = 5; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·5·(-108)
Δ = 2160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*5}=\frac{0-12\sqrt{15}}{10} =-\frac{12\sqrt{15}}{10} =-\frac{6\sqrt{15}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*5}=\frac{0+12\sqrt{15}}{10} =\frac{12\sqrt{15}}{10} =\frac{6\sqrt{15}}{5} $
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