7/3x-2=11/2x+5

Solution for 7/3x-2=11/2x+5 equation:

7/3x-2=11/2x+5

We move all terms to the left:

7/3x-2-(11/2x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

7/3x-11/2x-5-2=0

We calculate fractions


14x/6x^2+(-33x)/6x^2-5-2=0

We add all the numbers together, and all the variables

14x/6x^2+(-33x)/6x^2-7=0

We multiply all the terms by the denominator


14x+(-33x)-7*6x^2=0

Wy multiply elements

-42x^2+14x+(-33x)=0

We get rid of parentheses

-42x^2+14x-33x=0

We add all the numbers together, and all the variables

-42x^2-19x=0

a = -42; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-42)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-42}=\frac{0}{-84}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-42}=\frac{38}{-84}
=-19/42
$