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

-1150x^2+20x=0

a = -1150; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-1150)·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*-1150}=\frac{-40}{-2300}
=2/115
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-1150}=\frac{0}{-2300}
=0
$