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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x/24x^2+(-6x)/24x^2-2-5=0

We add all the numbers together, and all the variables

20x/24x^2+(-6x)/24x^2-7=0

We multiply all the terms by the denominator


20x+(-6x)-7*24x^2=0

Wy multiply elements

-168x^2+20x+(-6x)=0

We get rid of parentheses

-168x^2+20x-6x=0

We add all the numbers together, and all the variables

-168x^2+14x=0

a = -168; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-168)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-168}=\frac{-28}{-336}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-168}=\frac{0}{-336}
=0
$