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5n^2+7=48
We move all terms to the left:
5n^2+7-(48)=0
We add all the numbers together, and all the variables
5n^2-41=0
a = 5; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·5·(-41)
Δ = 820
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{205}}{2*5}=\frac{0-2\sqrt{205}}{10} =-\frac{2\sqrt{205}}{10} =-\frac{\sqrt{205}}{5} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{205}}{2*5}=\frac{0+2\sqrt{205}}{10} =\frac{2\sqrt{205}}{10} =\frac{\sqrt{205}}{5} $
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