4n^2-45n+11=0

Solution for 4n^2-45n+11=0 equation:

4n^2-45n+11=0

a = 4; b = -45; c = +11;
Δ = b2-4ac
Δ = -452-4·4·11
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-43}{2*4}=\frac{2}{8}
=1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+43}{2*4}=\frac{88}{8}
=11
$