(-7/4x)+(5/6x)=1

Solution for (-7/4x)+(5/6x)=1 equation:

(-7/4x)+(5/6x)=1

We move all terms to the left:

(-7/4x)+(5/6x)-(1)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-7/4x)+(+5/6x)-1=0

We get rid of parentheses

-7/4x+5/6x-1=0

We calculate fractions


(-42x)/24x^2+20x/24x^2-1=0

We multiply all the terms by the denominator


(-42x)+20x-1*24x^2=0

We add all the numbers together, and all the variables

20x+(-42x)-1*24x^2=0

Wy multiply elements

-24x^2+20x+(-42x)=0

We get rid of parentheses

-24x^2+20x-42x=0

We add all the numbers together, and all the variables

-24x^2-22x=0

a = -24; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-24)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-24}=\frac{44}{-48}
=-11/12
$