4/3x-7=11-3/5x

Solution for 4/3x-7=11-3/5x equation:

4/3x-7=11-3/5x

We move all terms to the left:

4/3x-7-(11-3/5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-3/5x+11)-7=0

We get rid of parentheses

4/3x+3/5x-11-7=0

We calculate fractions


20x/15x^2+9x/15x^2-11-7=0

We add all the numbers together, and all the variables

20x/15x^2+9x/15x^2-18=0

We multiply all the terms by the denominator


20x+9x-18*15x^2=0

We add all the numbers together, and all the variables

29x-18*15x^2=0

Wy multiply elements

-270x^2+29x=0

a = -270; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-270)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-270}=\frac{-58}{-540}
=29/270
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-270}=\frac{0}{-540}
=0
$