5n2=33n+56

Solution for 5n2=33n+56 equation:

5n^2=33n+56

We move all terms to the left:

5n^2-(33n+56)=0

We get rid of parentheses

5n^2-33n-56=0

a = 5; b = -33; c = -56;
Δ = b2-4ac
Δ = -332-4·5·(-56)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-47}{2*5}=\frac{-14}{10}
=-1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+47}{2*5}=\frac{80}{10}
=8
$