14/x=126/2x+20

Solution for 14/x=126/2x+20 equation:

14/x=126/2x+20

We move all terms to the left:

14/x-(126/2x+20)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

14/x-126/2x-20=0

We calculate fractions


28x/2x^2+(-126x)/2x^2-20=0

We multiply all the terms by the denominator


28x+(-126x)-20*2x^2=0

Wy multiply elements

-40x^2+28x+(-126x)=0

We get rid of parentheses

-40x^2+28x-126x=0

We add all the numbers together, and all the variables

-40x^2-98x=0

a = -40; b = -98; c = 0;
Δ = b2-4ac
Δ = -982-4·(-40)·0
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-98}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+98}{2*-40}=\frac{196}{-80}
=-2+9/20
$