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-4n^2+9n=-7
We move all terms to the left:
-4n^2+9n-(-7)=0
We add all the numbers together, and all the variables
-4n^2+9n+7=0
a = -4; b = 9; c = +7;
Δ = b2-4ac
Δ = 92-4·(-4)·7
Δ = 193
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{-(9)-\sqrt{193}}{2*-4}=\frac{-9-\sqrt{193}}{-8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{193}}{2*-4}=\frac{-9+\sqrt{193}}{-8} $
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