16-6x^2=x^2

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

16-6x^2=x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-7x^2+16=0

a = -7; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-7)·16
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*-7}=\frac{0-8\sqrt{7}}{-14}
=-\frac{8\sqrt{7}}{-14}
=-\frac{4\sqrt{7}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*-7}=\frac{0+8\sqrt{7}}{-14}
=\frac{8\sqrt{7}}{-14}
=\frac{4\sqrt{7}}{-7}
$