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4n^2-15n+15=5
We move all terms to the left:
4n^2-15n+15-(5)=0
We add all the numbers together, and all the variables
4n^2-15n+10=0
a = 4; b = -15; c = +10;
Δ = b2-4ac
Δ = -152-4·4·10
Δ = 65
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{-(-15)-\sqrt{65}}{2*4}=\frac{15-\sqrt{65}}{8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{65}}{2*4}=\frac{15+\sqrt{65}}{8} $
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