-7/4x+1/3=5/3x-5

Solution for -7/4x+1/3=5/3x-5 equation:

-7/4x+1/3=5/3x-5

We move all terms to the left:

-7/4x+1/3-(5/3x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


We get rid of parentheses

-7/4x-5/3x+5+1/3=0

We calculate fractions


(-189x)/108x^2+(-20x)/108x^2+4x/108x^2+5=0

We multiply all the terms by the denominator


(-189x)+(-20x)+4x+5*108x^2=0

We add all the numbers together, and all the variables

4x+(-189x)+(-20x)+5*108x^2=0

Wy multiply elements

540x^2+4x+(-189x)+(-20x)=0

We get rid of parentheses

540x^2+4x-189x-20x=0

We add all the numbers together, and all the variables

540x^2-205x=0

a = 540; b = -205; c = 0;
Δ = b2-4ac
Δ = -2052-4·540·0
Δ = 42025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42025}=205$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-205)-205}{2*540}=\frac{0}{1080}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-205)+205}{2*540}=\frac{410}{1080}
=41/108
$