(7)/(2x)+(6)/(4x)=(5x)/(4)

Solution for (7)/(2x)+(6)/(4x)=(5x)/(4) equation:

(7)/(2x)+(6)/(4x)=(5x)/(4)

We move all terms to the left:

(7)/(2x)+(6)/(4x)-((5x)/(4))=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x+6/4x-(+5x/4)=0

We get rid of parentheses

7/2x+6/4x-5x/4=0

We calculate fractions


(-10x^2)/128x^2+448x/128x^2+12x/128x^2=0

We multiply all the terms by the denominator


(-10x^2)+448x+12x=0

We add all the numbers together, and all the variables

(-10x^2)+460x=0

We get rid of parentheses

-10x^2+460x=0

a = -10; b = 460; c = 0;
Δ = b2-4ac
Δ = 4602-4·(-10)·0
Δ = 211600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{211600}=460$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(460)-460}{2*-10}=\frac{-920}{-20}
=+46
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(460)+460}{2*-10}=\frac{0}{-20}
=0
$