1/x+5=3/4x-6

Solution for 1/x+5=3/4x-6 equation:

1/x+5=3/4x-6

We move all terms to the left:

1/x+5-(3/4x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

1/x-3/4x+6+5=0

We calculate fractions


4x/4x^2+(-3x)/4x^2+6+5=0

We add all the numbers together, and all the variables

4x/4x^2+(-3x)/4x^2+11=0

We multiply all the terms by the denominator


4x+(-3x)+11*4x^2=0

Wy multiply elements

44x^2+4x+(-3x)=0

We get rid of parentheses

44x^2+4x-3x=0

We add all the numbers together, and all the variables

44x^2+x=0

a = 44; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·44·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*44}=\frac{-2}{88}
=-1/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*44}=\frac{0}{88}
=0
$