4n^2-17n=15

Solution for 4n^2-17n=15 equation:

4n^2-17n=15

We move all terms to the left:

4n^2-17n-(15)=0

a = 4; b = -17; c = -15;
Δ = b2-4ac
Δ = -172-4·4·(-15)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-23}{2*4}=\frac{-6}{8}
=-3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+23}{2*4}=\frac{40}{8}
=5
$