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5n^2-108=7n
We move all terms to the left:
5n^2-108-(7n)=0
a = 5; b = -7; c = -108;
Δ = b2-4ac
Δ = -72-4·5·(-108)
Δ = 2209
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2209}=47$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-47}{2*5}=\frac{-40}{10} =-4 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+47}{2*5}=\frac{54}{10} =5+2/5 $
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