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15n(n+2)=7n-4
We move all terms to the left:
15n(n+2)-(7n-4)=0
We multiply parentheses
15n^2+30n-(7n-4)=0
We get rid of parentheses
15n^2+30n-7n+4=0
We add all the numbers together, and all the variables
15n^2+23n+4=0
a = 15; b = 23; c = +4;
Δ = b2-4ac
Δ = 232-4·15·4
Δ = 289
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{289}=17$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-17}{2*15}=\frac{-40}{30} =-1+1/3 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+17}{2*15}=\frac{-6}{30} =-1/5 $
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