x^2+4x^2=2400

Solution for x^2+4x^2=2400 equation:

x^2+4x^2=2400

We move all terms to the left:

x^2+4x^2-(2400)=0

We add all the numbers together, and all the variables

5x^2-2400=0

a = 5; b = 0; c = -2400;
Δ = b2-4ac
Δ = 02-4·5·(-2400)
Δ = 48000
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:

$\sqrt{\Delta}=\sqrt{48000}=\sqrt{1600*30}=\sqrt{1600}*\sqrt{30}=40\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{30}}{2*5}=\frac{0-40\sqrt{30}}{10}
=-\frac{40\sqrt{30}}{10}
=-4\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{30}}{2*5}=\frac{0+40\sqrt{30}}{10}
=\frac{40\sqrt{30}}{10}
=4\sqrt{30}
$