4/x+5/4x=8

Solution for 4/x+5/4x=8 equation:

4/x+5/4x=8

We move all terms to the left:

4/x+5/4x-(8)=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^2-8=0

We multiply all the terms by the denominator


16x+5x-8*4x^2=0

We add all the numbers together, and all the variables

21x-8*4x^2=0

Wy multiply elements

-32x^2+21x=0

a = -32; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-32)·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*-32}=\frac{-42}{-64}
=21/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-32}=\frac{0}{-64}
=0
$