6n^2-15=6(5)^2-15

Solution for 6n^2-15=6(5)^2-15 equation:

6n^2-15=6(5)^2-15

We move all terms to the left:

6n^2-15-(6(5)^2-15)=0

We add all the numbers together, and all the variables

6n^2-4225=0

a = 6; b = 0; c = -4225;
Δ = b2-4ac
Δ = 02-4·6·(-4225)
Δ = 101400
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:

$\sqrt{\Delta}=\sqrt{101400}=\sqrt{16900*6}=\sqrt{16900}*\sqrt{6}=130\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-130\sqrt{6}}{2*6}=\frac{0-130\sqrt{6}}{12}
=-\frac{130\sqrt{6}}{12}
=-\frac{65\sqrt{6}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+130\sqrt{6}}{2*6}=\frac{0+130\sqrt{6}}{12}
=\frac{130\sqrt{6}}{12}
=\frac{65\sqrt{6}}{6}
$