13n^2-13n/6=0

Solution for 13n^2-13n/6=0 equation:

13n^2-13n/6=0

We multiply all the terms by the denominator


13n^2*6-13n=0

Wy multiply elements

78n^2-13n=0

a = 78; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·78·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*78}=\frac{0}{156}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*78}=\frac{26}{156}
=1/6
$