3/7x-1/2x=3/2x-2

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Solution for 3/7x-1/2x=3/2x-2 equation: 



3/7x-1/2x=3/2x-2

We move all terms to the left:

3/7x-1/2x-(3/2x-2)=0



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R





Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R





Domain of the equation: 2x-2)!=0

x∈R



We get rid of parentheses

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

We calculate fractions


6x/14x^2+(-21x-1)/14x^2+2=0

We multiply all the terms by the denominator


6x+(-21x-1)+2*14x^2=0

Wy multiply elements

28x^2+6x+(-21x-1)=0

We get rid of parentheses

28x^2+6x-21x-1=0

We add all the numbers together, and all the variables

28x^2-15x-1=0

a = 28; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·28·(-1)
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{337}}{2*28}=\frac{15-\sqrt{337}}{56}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{337}}{2*28}=\frac{15+\sqrt{337}}{56}
$

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