7/5x-2/3x=20

Solution for 7/5x-2/3x=20 equation:

7/5x-2/3x=20

We move all terms to the left:

7/5x-2/3x-(20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


21x/15x^2+(-10x)/15x^2-20=0

We multiply all the terms by the denominator


21x+(-10x)-20*15x^2=0

Wy multiply elements

-300x^2+21x+(-10x)=0

We get rid of parentheses

-300x^2+21x-10x=0

We add all the numbers together, and all the variables

-300x^2+11x=0

a = -300; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-300)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-300}=\frac{-22}{-600}
=11/300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-300}=\frac{0}{-600}
=0
$