3/5x-4/3=1/2x-1

Solution for 3/5x-4/3=1/2x-1 equation:

3/5x-4/3=1/2x-1

We move all terms to the left:

3/5x-4/3-(1/2x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

3/5x-1/2x+1-4/3=0

We calculate fractions


(-80x^2)/90x^2+54x/90x^2+(-45x)/90x^2+1=0

We multiply all the terms by the denominator


(-80x^2)+54x+(-45x)+1*90x^2=0

Wy multiply elements

(-80x^2)+90x^2+54x+(-45x)=0

We get rid of parentheses

-80x^2+90x^2+54x-45x=0

We add all the numbers together, and all the variables

10x^2+9x=0

a = 10; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·10·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*10}=\frac{-18}{20}
=-9/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*10}=\frac{0}{20}
=0
$