2x+2/11x=40

Solution for 2x+2/11x=40 equation:

2x+2/11x=40

We move all terms to the left:

2x+2/11x-(40)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We multiply all the terms by the denominator


2x*11x-40*11x+2=0

Wy multiply elements

22x^2-440x+2=0

a = 22; b = -440; c = +2;
Δ = b2-4ac
Δ = -4402-4·22·2
Δ = 193424
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:

$\sqrt{\Delta}=\sqrt{193424}=\sqrt{16*12089}=\sqrt{16}*\sqrt{12089}=4\sqrt{12089}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-440)-4\sqrt{12089}}{2*22}=\frac{440-4\sqrt{12089}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-440)+4\sqrt{12089}}{2*22}=\frac{440+4\sqrt{12089}}{44}
$