2x+40=2/318x

Solution for 2x+40=2/318x equation:

2x+40=2/318x

We move all terms to the left:

2x+40-(2/318x)=0


Domain of the equation: 318x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/318x)+40=0

We get rid of parentheses

2x-2/318x+40=0

We multiply all the terms by the denominator


2x*318x+40*318x-2=0

Wy multiply elements

636x^2+12720x-2=0

a = 636; b = 12720; c = -2;
Δ = b2-4ac
Δ = 127202-4·636·(-2)
Δ = 161803488
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:

$\sqrt{\Delta}=\sqrt{161803488}=\sqrt{784*206382}=\sqrt{784}*\sqrt{206382}=28\sqrt{206382}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12720)-28\sqrt{206382}}{2*636}=\frac{-12720-28\sqrt{206382}}{1272}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12720)+28\sqrt{206382}}{2*636}=\frac{-12720+28\sqrt{206382}}{1272}
$