2x+40=2/14x

Solution for 2x+40=2/14x equation:

2x+40=2/14x

We move all terms to the left:

2x+40-(2/14x)=0


Domain of the equation: 14x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/14x)+40=0

We get rid of parentheses

2x-2/14x+40=0

We multiply all the terms by the denominator


2x*14x+40*14x-2=0

Wy multiply elements

28x^2+560x-2=0

a = 28; b = 560; c = -2;
Δ = b2-4ac
Δ = 5602-4·28·(-2)
Δ = 313824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{313824}=\sqrt{16*19614}=\sqrt{16}*\sqrt{19614}=4\sqrt{19614}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(560)-4\sqrt{19614}}{2*28}=\frac{-560-4\sqrt{19614}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(560)+4\sqrt{19614}}{2*28}=\frac{-560+4\sqrt{19614}}{56}
$