3x^2+1-47=0

Solution for 3x^2+1-47=0 equation:

3x^2+1-47=0

We add all the numbers together, and all the variables

3x^2-46=0

a = 3; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·3·(-46)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{138}}{2*3}=\frac{0-2\sqrt{138}}{6}
=-\frac{2\sqrt{138}}{6}
=-\frac{\sqrt{138}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{138}}{2*3}=\frac{0+2\sqrt{138}}{6}
=\frac{2\sqrt{138}}{6}
=\frac{\sqrt{138}}{3}
$