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3n^2+5n=n2-7n-10
We move all terms to the left:
3n^2+5n-(n2-7n-10)=0
We add all the numbers together, and all the variables
3n^2-(+n^2-7n-10)+5n=0
We get rid of parentheses
3n^2-n^2+7n+5n+10=0
We add all the numbers together, and all the variables
2n^2+12n+10=0
a = 2; b = 12; c = +10;
Δ = b2-4ac
Δ = 122-4·2·10
Δ = 64
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{64}=8$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*2}=\frac{-20}{4} =-5 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*2}=\frac{-4}{4} =-1 $
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