X^2+0.5x^2=16

Solution for X^2+0.5x^2=16 equation:

X^2+0.5X^2=16

We move all terms to the left:

X^2+0.5X^2-(16)=0

We add all the numbers together, and all the variables

1.5X^2-16=0

a = 1.5; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1.5·(-16)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*1.5}=\frac{0-4\sqrt{6}}{3}
=-\frac{4\sqrt{6}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*1.5}=\frac{0+4\sqrt{6}}{3}
=\frac{4\sqrt{6}}{3}
$