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18x^2+15=103
We move all terms to the left:
18x^2+15-(103)=0
We add all the numbers together, and all the variables
18x^2-88=0
a = 18; b = 0; c = -88;
Δ = b2-4ac
Δ = 02-4·18·(-88)
Δ = 6336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{11}}{2*18}=\frac{0-24\sqrt{11}}{36} =-\frac{24\sqrt{11}}{36} =-\frac{2\sqrt{11}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{11}}{2*18}=\frac{0+24\sqrt{11}}{36} =\frac{24\sqrt{11}}{36} =\frac{2\sqrt{11}}{3} $
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