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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


(-220x^2)/490x^2+196x/490x^2+(-735x)/490x^2=0

We multiply all the terms by the denominator


(-220x^2)+196x+(-735x)=0

We get rid of parentheses

-220x^2+196x-735x=0

We add all the numbers together, and all the variables

-220x^2-539x=0

a = -220; b = -539; c = 0;
Δ = b2-4ac
Δ = -5392-4·(-220)·0
Δ = 290521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{290521}=539$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-539)-539}{2*-220}=\frac{0}{-440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-539)+539}{2*-220}=\frac{1078}{-440}
=-2+9/20
$