3/4x-2/3=-5/3x+7

Solution for 3/4x-2/3=-5/3x+7 equation:

3/4x-2/3=-5/3x+7

We move all terms to the left:

3/4x-2/3-(-5/3x+7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/4x+5/3x-7-2/3=0

We calculate fractions


81x/108x^2+20x/108x^2+(-8x)/108x^2-7=0

We multiply all the terms by the denominator


81x+20x+(-8x)-7*108x^2=0

We add all the numbers together, and all the variables

101x+(-8x)-7*108x^2=0

Wy multiply elements

-756x^2+101x+(-8x)=0

We get rid of parentheses

-756x^2+101x-8x=0

We add all the numbers together, and all the variables

-756x^2+93x=0

a = -756; b = 93; c = 0;
Δ = b2-4ac
Δ = 932-4·(-756)·0
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-93}{2*-756}=\frac{-186}{-1512}
=31/252
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+93}{2*-756}=\frac{0}{-1512}
=0
$