4x^2+3=395

Solution for 4x^2+3=395 equation:

4x^2+3=395

We move all terms to the left:

4x^2+3-(395)=0

We add all the numbers together, and all the variables

4x^2-392=0

a = 4; b = 0; c = -392;
Δ = b2-4ac
Δ = 02-4·4·(-392)
Δ = 6272
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:

$\sqrt{\Delta}=\sqrt{6272}=\sqrt{3136*2}=\sqrt{3136}*\sqrt{2}=56\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56\sqrt{2}}{2*4}=\frac{0-56\sqrt{2}}{8}
=-\frac{56\sqrt{2}}{8}
=-7\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56\sqrt{2}}{2*4}=\frac{0+56\sqrt{2}}{8}
=\frac{56\sqrt{2}}{8}
=7\sqrt{2}
$