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4n^2+5n-51=0
a = 4; b = 5; c = -51;
Δ = b2-4ac
Δ = 52-4·4·(-51)
Δ = 841
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{841}=29$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*4}=\frac{-34}{8} =-4+1/4 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*4}=\frac{24}{8} =3 $
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