1/x+5/2x=11

Solution for 1/x+5/2x=11 equation:

1/x+5/2x=11

We move all terms to the left:

1/x+5/2x-(11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


2x/2x^2+5x/2x^2-11=0

We multiply all the terms by the denominator


2x+5x-11*2x^2=0

We add all the numbers together, and all the variables

7x-11*2x^2=0

Wy multiply elements

-22x^2+7x=0

a = -22; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-22)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-22}=\frac{-14}{-44}
=7/22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-22}=\frac{0}{-44}
=0
$