2x^2+3=47

Solution for 2x^2+3=47 equation:

2x^2+3=47

We move all terms to the left:

2x^2+3-(47)=0

We add all the numbers together, and all the variables

2x^2-44=0

a = 2; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·2·(-44)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*2}=\frac{0-4\sqrt{22}}{4}
=-\frac{4\sqrt{22}}{4}
=-\sqrt{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*2}=\frac{0+4\sqrt{22}}{4}
=\frac{4\sqrt{22}}{4}
=\sqrt{22}
$