3x^2=101

Solution for 3x^2=101 equation:

3x^2=101

We move all terms to the left:

3x^2-(101)=0

a = 3; b = 0; c = -101;
Δ = b2-4ac
Δ = 02-4·3·(-101)
Δ = 1212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1212}=\sqrt{4*303}=\sqrt{4}*\sqrt{303}=2\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{303}}{2*3}=\frac{0-2\sqrt{303}}{6}
=-\frac{2\sqrt{303}}{6}
=-\frac{\sqrt{303}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{303}}{2*3}=\frac{0+2\sqrt{303}}{6}
=\frac{2\sqrt{303}}{6}
=\frac{\sqrt{303}}{3}
$