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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


(-288x^2)/108x^2+270x/108x^2+90x/108x^2+4=0

We multiply all the terms by the denominator


(-288x^2)+270x+90x+4*108x^2=0

We add all the numbers together, and all the variables

(-288x^2)+360x+4*108x^2=0

Wy multiply elements

(-288x^2)+432x^2+360x=0

We get rid of parentheses

-288x^2+432x^2+360x=0

We add all the numbers together, and all the variables

144x^2+360x=0

a = 144; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·144·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*144}=\frac{-720}{288}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*144}=\frac{0}{288}
=0
$