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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 7x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


21x/14x^2+(-2x)/14x^2-7+2=0

We add all the numbers together, and all the variables

21x/14x^2+(-2x)/14x^2-5=0

We multiply all the terms by the denominator


21x+(-2x)-5*14x^2=0

Wy multiply elements

-70x^2+21x+(-2x)=0

We get rid of parentheses

-70x^2+21x-2x=0

We add all the numbers together, and all the variables

-70x^2+19x=0

a = -70; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-70)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-70}=\frac{-38}{-140}
=19/70
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-70}=\frac{0}{-140}
=0
$