3n^2=9.75

Solution for 3n^2=9.75 equation:

3n^2=9.75

We move all terms to the left:

3n^2-(9.75)=0

We add all the numbers together, and all the variables

3n^2-9.75=0

a = 3; b = 0; c = -9.75;
Δ = b2-4ac
Δ = 02-4·3·(-9.75)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{13}}{2*3}=\frac{0-3\sqrt{13}}{6}
=-\frac{3\sqrt{13}}{6}
=-\frac{\sqrt{13}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{13}}{2*3}=\frac{0+3\sqrt{13}}{6}
=\frac{3\sqrt{13}}{6}
=\frac{\sqrt{13}}{2}
$