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5n^2-7=488
We move all terms to the left:
5n^2-7-(488)=0
We add all the numbers together, and all the variables
5n^2-495=0
a = 5; b = 0; c = -495;
Δ = b2-4ac
Δ = 02-4·5·(-495)
Δ = 9900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9900}=\sqrt{900*11}=\sqrt{900}*\sqrt{11}=30\sqrt{11}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{11}}{2*5}=\frac{0-30\sqrt{11}}{10} =-\frac{30\sqrt{11}}{10} =-3\sqrt{11} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{11}}{2*5}=\frac{0+30\sqrt{11}}{10} =\frac{30\sqrt{11}}{10} =3\sqrt{11} $
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