2x^2-6(x^2-2)=-16

Solution for 2x^2-6(x^2-2)=-16 equation:

2x^2-6(x^2-2)=-16

We move all terms to the left:

2x^2-6(x^2-2)-(-16)=0

We add all the numbers together, and all the variables

2x^2-6(x^2-2)+16=0

We multiply parentheses

2x^2-6x^2+12+16=0

We add all the numbers together, and all the variables

-4x^2+28=0

a = -4; b = 0; c = +28;
Δ = b2-4ac
Δ = 02-4·(-4)·28
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*-4}=\frac{0-8\sqrt{7}}{-8}
=-\frac{8\sqrt{7}}{-8}
=-\frac{\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*-4}=\frac{0+8\sqrt{7}}{-8}
=\frac{8\sqrt{7}}{-8}
=\frac{\sqrt{7}}{-1}
$