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-3n^2-11n+35=7-4n^2
We move all terms to the left:
-3n^2-11n+35-(7-4n^2)=0
We get rid of parentheses
-3n^2+4n^2-11n-7+35=0
We add all the numbers together, and all the variables
n^2-11n+28=0
a = 1; b = -11; c = +28;
Δ = b2-4ac
Δ = -112-4·1·28
Δ = 9
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{9}=3$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3}{2*1}=\frac{8}{2} =4 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3}{2*1}=\frac{14}{2} =7 $
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