x(30-0.5x)=0

Solution for x(30-0.5x)=0 equation:

x(30-0.5x)=0

We add all the numbers together, and all the variables

x(-0.5x+30)=0

We multiply parentheses

0x^2+30x=0

We add all the numbers together, and all the variables

x^2+30x=0

a = 1; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·1·0
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{-(30)-30}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*1}=\frac{0}{2}
=0
$