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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x/24x^2+(-18x)/24x^2+1+5=0

We add all the numbers together, and all the variables

20x/24x^2+(-18x)/24x^2+6=0

We multiply all the terms by the denominator


20x+(-18x)+6*24x^2=0

Wy multiply elements

144x^2+20x+(-18x)=0

We get rid of parentheses

144x^2+20x-18x=0

We add all the numbers together, and all the variables

144x^2+2x=0

a = 144; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·144·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*144}=\frac{-4}{288}
=-1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*144}=\frac{0}{288}
=0
$