4x^2-342=0

Solution for 4x^2-342=0 equation:

4x^2-342=0

a = 4; b = 0; c = -342;
Δ = b2-4ac
Δ = 02-4·4·(-342)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{38}}{2*4}=\frac{0-12\sqrt{38}}{8}
=-\frac{12\sqrt{38}}{8}
=-\frac{3\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{38}}{2*4}=\frac{0+12\sqrt{38}}{8}
=\frac{12\sqrt{38}}{8}
=\frac{3\sqrt{38}}{2}
$