-4z^2=-16+6z^2

Solution for -4z^2=-16+6z^2 equation:

-4z^2=-16+6z^2

We move all terms to the left:

-4z^2-(-16+6z^2)=0

We get rid of parentheses

-4z^2-6z^2+16=0

We add all the numbers together, and all the variables

-10z^2+16=0

a = -10; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-10)·16
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-10}=\frac{0-8\sqrt{10}}{-20}
=-\frac{8\sqrt{10}}{-20}
=-\frac{2\sqrt{10}}{-5}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-10}=\frac{0+8\sqrt{10}}{-20}
=\frac{8\sqrt{10}}{-20}
=\frac{2\sqrt{10}}{-5}
$