4x^2+2x^2=400

Solution for 4x^2+2x^2=400 equation:

4x^2+2x^2=400

We move all terms to the left:

4x^2+2x^2-(400)=0

We add all the numbers together, and all the variables

6x^2-400=0

a = 6; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·6·(-400)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*6}=\frac{0-40\sqrt{6}}{12}
=-\frac{40\sqrt{6}}{12}
=-\frac{10\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*6}=\frac{0+40\sqrt{6}}{12}
=\frac{40\sqrt{6}}{12}
=\frac{10\sqrt{6}}{3}
$