12/7x+3/2x=15/14

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Solution for 12/7x+3/2x=15/14 equation: 



12/7x+3/2x=15/14

We move all terms to the left:

12/7x+3/2x-(15/14)=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



We add all the numbers together, and all the variables

12/7x+3/2x-(+15/14)=0

We get rid of parentheses

12/7x+3/2x-15/14=0

We calculate fractions


(-420x^2)/196x^2+336x/196x^2+294x/196x^2=0

We multiply all the terms by the denominator


(-420x^2)+336x+294x=0

We add all the numbers together, and all the variables

(-420x^2)+630x=0

We get rid of parentheses

-420x^2+630x=0

a = -420; b = 630; c = 0;
Δ = b2-4ac
Δ = 6302-4·(-420)·0
Δ = 396900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{396900}=630$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(630)-630}{2*-420}=\frac{-1260}{-840}
=1+1/2
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(630)+630}{2*-420}=\frac{0}{-840}
=0
$

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