20/3x-2=28/7x-3

Solution for 20/3x-2=28/7x-3 equation:

20/3x-2=28/7x-3

We move all terms to the left:

20/3x-2-(28/7x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x-3)!=0

x∈R


We get rid of parentheses

20/3x-28/7x+3-2=0

We calculate fractions


140x/21x^2+(-84x)/21x^2+3-2=0

We add all the numbers together, and all the variables

140x/21x^2+(-84x)/21x^2+1=0

We multiply all the terms by the denominator


140x+(-84x)+1*21x^2=0

Wy multiply elements

21x^2+140x+(-84x)=0

We get rid of parentheses

21x^2+140x-84x=0

We add all the numbers together, and all the variables

21x^2+56x=0

a = 21; b = 56; c = 0;
Δ = b2-4ac
Δ = 562-4·21·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-56}{2*21}=\frac{-112}{42}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+56}{2*21}=\frac{0}{42}
=0
$