6n^2-25-9=0

Solution for 6n^2-25-9=0 equation:

6n^2-25-9=0

We add all the numbers together, and all the variables

6n^2-34=0

a = 6; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·6·(-34)
Δ = 816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*6}=\frac{0-4\sqrt{51}}{12}
=-\frac{4\sqrt{51}}{12}
=-\frac{\sqrt{51}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*6}=\frac{0+4\sqrt{51}}{12}
=\frac{4\sqrt{51}}{12}
=\frac{\sqrt{51}}{3}
$