4x^2+3=323

Solution for 4x^2+3=323 equation:

4x^2+3=323

We move all terms to the left:

4x^2+3-(323)=0

We add all the numbers together, and all the variables

4x^2-320=0

a = 4; b = 0; c = -320;
Δ = b2-4ac
Δ = 02-4·4·(-320)
Δ = 5120
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:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{5}}{2*4}=\frac{0-32\sqrt{5}}{8}
=-\frac{32\sqrt{5}}{8}
=-4\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{5}}{2*4}=\frac{0+32\sqrt{5}}{8}
=\frac{32\sqrt{5}}{8}
=4\sqrt{5}
$