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500=15+5x^2
We move all terms to the left:
500-(15+5x^2)=0
We get rid of parentheses
-5x^2-15+500=0
We add all the numbers together, and all the variables
-5x^2+485=0
a = -5; b = 0; c = +485;
Δ = b2-4ac
Δ = 02-4·(-5)·485
Δ = 9700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9700}=\sqrt{100*97}=\sqrt{100}*\sqrt{97}=10\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{97}}{2*-5}=\frac{0-10\sqrt{97}}{-10} =-\frac{10\sqrt{97}}{-10} =-\frac{\sqrt{97}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{97}}{2*-5}=\frac{0+10\sqrt{97}}{-10} =\frac{10\sqrt{97}}{-10} =\frac{\sqrt{97}}{-1} $
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