150/x=0,5x

Solution for 150/x=0,5x equation:

150/x=0.5x

We move all terms to the left:

150/x-(0.5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

150/x-(+0.5x)=0

We get rid of parentheses

150/x-0.5x=0

We multiply all the terms by the denominator


-(0.5x)*x+150=0

We add all the numbers together, and all the variables

-(+0.5x)*x+150=0

We multiply parentheses

-0x^2+150=0

We add all the numbers together, and all the variables

-1x^2+150=0

a = -1; b = 0; c = +150;
Δ = b2-4ac
Δ = 02-4·(-1)·150
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-1}=\frac{0-10\sqrt{6}}{-2}
=-\frac{10\sqrt{6}}{-2}
=-\frac{5\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-1}=\frac{0+10\sqrt{6}}{-2}
=\frac{10\sqrt{6}}{-2}
=\frac{5\sqrt{6}}{-1}
$