x^2+0.5x^2=80

Solution for x^2+0.5x^2=80 equation:

x^2+0.5x^2=80

We move all terms to the left:

x^2+0.5x^2-(80)=0

We add all the numbers together, and all the variables

1.5x^2-80=0

a = 1.5; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·1.5·(-80)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*1.5}=\frac{0-4\sqrt{30}}{3}
=-\frac{4\sqrt{30}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*1.5}=\frac{0+4\sqrt{30}}{3}
=\frac{4\sqrt{30}}{3}
$