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4n^2+5n=7
We move all terms to the left:
4n^2+5n-(7)=0
a = 4; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·4·(-7)
Δ = 137
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{137}}{2*4}=\frac{-5-\sqrt{137}}{8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{137}}{2*4}=\frac{-5+\sqrt{137}}{8} $
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