x^2+.5x^2=150

Solution for x^2+.5x^2=150 equation:

x^2+.5x^2=150

We move all terms to the left:

x^2+.5x^2-(150)=0

We add all the numbers together, and all the variables

1.5x^2-150=0

a = 1.5; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·1.5·(-150)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*1.5}=\frac{-30}{3}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*1.5}=\frac{30}{3}
=10
$