3/5x+3/2=7/10x

Solution for 3/5x+3/2=7/10x equation:

3/5x+3/2=7/10x

We move all terms to the left:

3/5x+3/2-(7/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(+7/10x)+3/2=0

We get rid of parentheses

3/5x-7/10x+3/2=0

We calculate fractions


150x^2/200x^2+120x/200x^2+(-140x)/200x^2=0

We multiply all the terms by the denominator


150x^2+120x+(-140x)=0

We get rid of parentheses

150x^2+120x-140x=0

We add all the numbers together, and all the variables

150x^2-20x=0

a = 150; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·150·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*150}=\frac{40}{300}
=2/15
$