7/4x+2/x=20

Solution for 7/4x+2/x=20 equation:

7/4x+2/x=20

We move all terms to the left:

7/4x+2/x-(20)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


7x/4x^2+8x/4x^2-20=0

We multiply all the terms by the denominator


7x+8x-20*4x^2=0

We add all the numbers together, and all the variables

15x-20*4x^2=0

Wy multiply elements

-80x^2+15x=0

a = -80; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-80)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-80}=\frac{-30}{-160}
=3/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-80}=\frac{0}{-160}
=0
$