4x^2-6=346

Solution for 4x^2-6=346 equation:

4x^2-6=346

We move all terms to the left:

4x^2-6-(346)=0

We add all the numbers together, and all the variables

4x^2-352=0

a = 4; b = 0; c = -352;
Δ = b2-4ac
Δ = 02-4·4·(-352)
Δ = 5632
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:

$\sqrt{\Delta}=\sqrt{5632}=\sqrt{256*22}=\sqrt{256}*\sqrt{22}=16\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{22}}{2*4}=\frac{0-16\sqrt{22}}{8}
=-\frac{16\sqrt{22}}{8}
=-2\sqrt{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{22}}{2*4}=\frac{0+16\sqrt{22}}{8}
=\frac{16\sqrt{22}}{8}
=2\sqrt{22}
$