4x+49=22/x

Solution for 4x+49=22/x equation:

4x+49=22/x

We move all terms to the left:

4x+49-(22/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+22/x)+49=0

We get rid of parentheses

4x-22/x+49=0

We multiply all the terms by the denominator


4x*x+49*x-22=0

We add all the numbers together, and all the variables

49x+4x*x-22=0

Wy multiply elements

4x^2+49x-22=0

a = 4; b = 49; c = -22;
Δ = b2-4ac
Δ = 492-4·4·(-22)
Δ = 2753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-\sqrt{2753}}{2*4}=\frac{-49-\sqrt{2753}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{2753}}{2*4}=\frac{-49+\sqrt{2753}}{8}
$