11/20x+14=9/10x

Solution for 11/20x+14=9/10x equation:

11/20x+14=9/10x

We move all terms to the left:

11/20x+14-(9/10x)=0


Domain of the equation: 20x!=0

x!=0/20

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

11/20x-(+9/10x)+14=0

We get rid of parentheses

11/20x-9/10x+14=0

We calculate fractions


110x/200x^2+(-180x)/200x^2+14=0

We multiply all the terms by the denominator


110x+(-180x)+14*200x^2=0

Wy multiply elements

2800x^2+110x+(-180x)=0

We get rid of parentheses

2800x^2+110x-180x=0

We add all the numbers together, and all the variables

2800x^2-70x=0

a = 2800; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·2800·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*2800}=\frac{0}{5600}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*2800}=\frac{140}{5600}
=1/40
$