3/x+4/2x=5/4

Solution for 3/x+4/2x=5/4 equation:

3/x+4/2x=5/4

We move all terms to the left:

3/x+4/2x-(5/4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/x+4/2x-(+5/4)=0

We get rid of parentheses

3/x+4/2x-5/4=0

We calculate fractions


(-20x^2)/32x^2+96x/32x^2+64x/32x^2=0

We multiply all the terms by the denominator


(-20x^2)+96x+64x=0

We add all the numbers together, and all the variables

(-20x^2)+160x=0

We get rid of parentheses

-20x^2+160x=0

a = -20; b = 160; c = 0;
Δ = b2-4ac
Δ = 1602-4·(-20)·0
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-160}{2*-20}=\frac{-320}{-40}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+160}{2*-20}=\frac{0}{-40}
=0
$