3/4x+1=5/6x-2

Solution for 3/4x+1=5/6x-2 equation:

3/4x+1=5/6x-2

We move all terms to the left:

3/4x+1-(5/6x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x-2)!=0

x∈R


We get rid of parentheses

3/4x-5/6x+2+1=0

We calculate fractions


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

We add all the numbers together, and all the variables

18x/24x^2+(-20x)/24x^2+3=0

We multiply all the terms by the denominator


18x+(-20x)+3*24x^2=0

Wy multiply elements

72x^2+18x+(-20x)=0

We get rid of parentheses

72x^2+18x-20x=0

We add all the numbers together, and all the variables

72x^2-2x=0

a = 72; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·72·0
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*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*72}=\frac{4}{144}
=1/36
$