7/10x=3/20x+2

Solution for 7/10x=3/20x+2 equation:

7/10x=3/20x+2

We move all terms to the left:

7/10x-(3/20x+2)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 20x+2)!=0

x∈R


We get rid of parentheses

7/10x-3/20x-2=0

We calculate fractions


140x/200x^2+(-30x)/200x^2-2=0

We multiply all the terms by the denominator


140x+(-30x)-2*200x^2=0

Wy multiply elements

-400x^2+140x+(-30x)=0

We get rid of parentheses

-400x^2+140x-30x=0

We add all the numbers together, and all the variables

-400x^2+110x=0

a = -400; b = 110; c = 0;
Δ = b2-4ac
Δ = 1102-4·(-400)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-110}{2*-400}=\frac{-220}{-800}
=11/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+110}{2*-400}=\frac{0}{-800}
=0
$