(5/6x)+(9/4x)=2

Solution for (5/6x)+(9/4x)=2 equation:

(5/6x)+(9/4x)=2

We move all terms to the left:

(5/6x)+(9/4x)-(2)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6x)+(+9/4x)-2=0

We get rid of parentheses

5/6x+9/4x-2=0

We calculate fractions


20x/24x^2+54x/24x^2-2=0

We multiply all the terms by the denominator


20x+54x-2*24x^2=0

We add all the numbers together, and all the variables

74x-2*24x^2=0

Wy multiply elements

-48x^2+74x=0

a = -48; b = 74; c = 0;
Δ = b2-4ac
Δ = 742-4·(-48)·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-74}{2*-48}=\frac{-148}{-96}
=1+13/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+74}{2*-48}=\frac{0}{-96}
=0
$