4n^2-21n+17=0

Solution for 4n^2-21n+17=0 equation:

4n^2-21n+17=0

a = 4; b = -21; c = +17;
Δ = b2-4ac
Δ = -212-4·4·17
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-13}{2*4}=\frac{8}{8}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+13}{2*4}=\frac{34}{8}
=4+1/4
$