10-1/(5)x=1/(10)x+3

Solution for 10-1/(5)x=1/(10)x+3 equation:

10-1/(5)x=1/(10)x+3

We move all terms to the left:

10-1/(5)x-(1/(10)x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+3)!=0

x∈R


We get rid of parentheses

-1/5x-1/10x-3+10=0

We calculate fractions


(-10x)/50x^2+(-5x)/50x^2-3+10=0

We add all the numbers together, and all the variables

(-10x)/50x^2+(-5x)/50x^2+7=0

We multiply all the terms by the denominator


(-10x)+(-5x)+7*50x^2=0

Wy multiply elements

350x^2+(-10x)+(-5x)=0

We get rid of parentheses

350x^2-10x-5x=0

We add all the numbers together, and all the variables

350x^2-15x=0

a = 350; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·350·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*350}=\frac{0}{700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*350}=\frac{30}{700}
=3/70
$