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5n^2+5n=288
We move all terms to the left:
5n^2+5n-(288)=0
a = 5; b = 5; c = -288;
Δ = b2-4ac
Δ = 52-4·5·(-288)
Δ = 5785
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{5785}}{2*5}=\frac{-5-\sqrt{5785}}{10} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{5785}}{2*5}=\frac{-5+\sqrt{5785}}{10} $
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