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

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Solution for 7/2x+3-5/3x-2=0 equation: 



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



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R





Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

7/2x-5/3x+1=0

We calculate fractions


21x/6x^2+(-10x)/6x^2+1=0

We multiply all the terms by the denominator


21x+(-10x)+1*6x^2=0

Wy multiply elements

6x^2+21x+(-10x)=0

We get rid of parentheses

6x^2+21x-10x=0

We add all the numbers together, and all the variables

6x^2+11x=0

a = 6; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·6·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*6}=\frac{-22}{12}
=-1+5/6
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*6}=\frac{0}{12}
=0
$

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