33n^2-82n+45=0

Solution for 33n^2-82n+45=0 equation:

33n^2-82n+45=0

a = 33; b = -82; c = +45;
Δ = b2-4ac
Δ = -822-4·33·45
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-28}{2*33}=\frac{54}{66}
=9/11
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+28}{2*33}=\frac{110}{66}
=1+2/3
$