4n^2-15n+15=5

Solution for 4n^2-15n+15=5 equation:

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}
$