4x^2-x^2-1600=0

Solution for 4x^2-x^2-1600=0 equation:

4x^2-x^2-1600=0

We add all the numbers together, and all the variables

3x^2-1600=0

a = 3; b = 0; c = -1600;
Δ = b2-4ac
Δ = 02-4·3·(-1600)
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*3}=\frac{0-80\sqrt{3}}{6}
=-\frac{80\sqrt{3}}{6}
=-\frac{40\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*3}=\frac{0+80\sqrt{3}}{6}
=\frac{80\sqrt{3}}{6}
=\frac{40\sqrt{3}}{3}
$