6n2-15=6(5)2-15

Solution for 6n2-15=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^2-15-637=0

We add all the numbers together, and all the variables

6n^2-652=0

a = 6; b = 0; c = -652;
Δ = b2-4ac
Δ = 02-4·6·(-652)
Δ = 15648
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:

$\sqrt{\Delta}=\sqrt{15648}=\sqrt{16*978}=\sqrt{16}*\sqrt{978}=4\sqrt{978}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{978}}{2*6}=\frac{0-4\sqrt{978}}{12}
=-\frac{4\sqrt{978}}{12}
=-\frac{\sqrt{978}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{978}}{2*6}=\frac{0+4\sqrt{978}}{12}
=\frac{4\sqrt{978}}{12}
=\frac{\sqrt{978}}{3}
$