-3x^2+2(16-x^2)=0

Solution for -3x^2+2(16-x^2)=0 equation:

-3x^2+2(16-x^2)=0

We multiply parentheses

-3x^2-2x^2+32=0

We add all the numbers together, and all the variables

-5x^2+32=0

a = -5; b = 0; c = +32;
Δ = b2-4ac
Δ = 02-4·(-5)·32
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-5}=\frac{0-8\sqrt{10}}{-10}
=-\frac{8\sqrt{10}}{-10}
=-\frac{4\sqrt{10}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-5}=\frac{0+8\sqrt{10}}{-10}
=\frac{8\sqrt{10}}{-10}
=\frac{4\sqrt{10}}{-5}
$