2n^2=13n-11

Solution for 2n^2=13n-11 equation:

2n^2=13n-11

We move all terms to the left:

2n^2-(13n-11)=0

We get rid of parentheses

2n^2-13n+11=0

a = 2; b = -13; c = +11;
Δ = b2-4ac
Δ = -132-4·2·11
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-9}{2*2}=\frac{4}{4}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+9}{2*2}=\frac{22}{4}
=5+1/2
$