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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


750x^2/200x^2+140x/200x^2+(-120x)/200x^2-2=0

We multiply all the terms by the denominator


750x^2+140x+(-120x)-2*200x^2=0

Wy multiply elements

750x^2-400x^2+140x+(-120x)=0

We get rid of parentheses

750x^2-400x^2+140x-120x=0

We add all the numbers together, and all the variables

350x^2+20x=0

a = 350; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·350·0
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*350}=\frac{-40}{700}
=-2/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*350}=\frac{0}{700}
=0
$