4x^2=420

Solution for 4x^2=420 equation:

4x^2=420

We move all terms to the left:

4x^2-(420)=0

a = 4; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·4·(-420)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{105}}{2*4}=\frac{0-8\sqrt{105}}{8}
=-\frac{8\sqrt{105}}{8}
=-\sqrt{105}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{105}}{2*4}=\frac{0+8\sqrt{105}}{8}
=\frac{8\sqrt{105}}{8}
=\sqrt{105}
$