x^2=0.5x^2+50

Solution for x^2=0.5x^2+50 equation:

x^2=0.5x^2+50

We move all terms to the left:

x^2-(0.5x^2+50)=0

We get rid of parentheses

x^2-0.5x^2-50=0

We add all the numbers together, and all the variables

0.5x^2-50=0

a = 0.5; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·0.5·(-50)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*0.5}=\frac{-10}{1}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*0.5}=\frac{10}{1}
=10
$