1/2x-3=22+1/7x

Solution for 1/2x-3=22+1/7x equation:

1/2x-3=22+1/7x

We move all terms to the left:

1/2x-3-(22+1/7x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(1/7x+22)-3=0

We get rid of parentheses

1/2x-1/7x-22-3=0

We calculate fractions


7x/14x^2+(-2x)/14x^2-22-3=0

We add all the numbers together, and all the variables

7x/14x^2+(-2x)/14x^2-25=0

We multiply all the terms by the denominator


7x+(-2x)-25*14x^2=0

Wy multiply elements

-350x^2+7x+(-2x)=0

We get rid of parentheses

-350x^2+7x-2x=0

We add all the numbers together, and all the variables

-350x^2+5x=0

a = -350; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-350)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-350}=\frac{-10}{-700}
=1/70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-350}=\frac{0}{-700}
=0
$