10-(1)/(15)x=(1)/(10)x

Solution for 10-(1)/(15)x=(1)/(10)x equation:

10-(1)/(15)x=(1)/(10)x

We move all terms to the left:

10-(1)/(15)x-((1)/(10)x)=0


Domain of the equation: 15x!=0

x!=0/15

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/15x-(+1/10x)+10=0

We get rid of parentheses

-1/15x-1/10x+10=0

We calculate fractions


(-10x)/150x^2+(-15x)/150x^2+10=0

We multiply all the terms by the denominator


(-10x)+(-15x)+10*150x^2=0

Wy multiply elements

1500x^2+(-10x)+(-15x)=0

We get rid of parentheses

1500x^2-10x-15x=0

We add all the numbers together, and all the variables

1500x^2-25x=0

a = 1500; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·1500·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*1500}=\frac{0}{3000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*1500}=\frac{50}{3000}
=1/60
$