2n^2-5n=13

Solution for 2n^2-5n=13 equation:

2n^2-5n=13

We move all terms to the left:

2n^2-5n-(13)=0

a = 2; b = -5; c = -13;
Δ = b2-4ac
Δ = -52-4·2·(-13)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{129}}{2*2}=\frac{5-\sqrt{129}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{129}}{2*2}=\frac{5+\sqrt{129}}{4}
$