4/x+5/4x=22

Solution for 4/x+5/4x=22 equation:

4/x+5/4x=22

We move all terms to the left:

4/x+5/4x-(22)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


16x/4x^2+5x/4x^2-22=0

We multiply all the terms by the denominator


16x+5x-22*4x^2=0

We add all the numbers together, and all the variables

21x-22*4x^2=0

Wy multiply elements

-88x^2+21x=0

a = -88; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-88)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-88}=\frac{-42}{-176}
=21/88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-88}=\frac{0}{-176}
=0
$