10-0.5x=1/3x

Solution for 10-0.5x=1/3x equation:

10-0.5x=1/3x

We move all terms to the left:

10-0.5x-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-0.5x-(+1/3x)+10=0

We get rid of parentheses

-0.5x-1/3x+10=0

We multiply all the terms by the denominator


-(0.5x)*3x+10*3x-1=0

We add all the numbers together, and all the variables

-(+0.5x)*3x+10*3x-1=0

We multiply parentheses

-0x^2+10*3x-1=0

Wy multiply elements

-0x^2+30x-1=0

We add all the numbers together, and all the variables

-1x^2+30x-1=0

a = -1; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·(-1)·(-1)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-8\sqrt{14}}{2*-1}=\frac{-30-8\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+8\sqrt{14}}{2*-1}=\frac{-30+8\sqrt{14}}{-2}
$