6/5x+12/5=5/6x+2

Solution for 6/5x+12/5=5/6x+2 equation:

6/5x+12/5=5/6x+2

We move all terms to the left:

6/5x+12/5-(5/6x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

6/5x-5/6x-2+12/5=0

We calculate fractions


36x/750x^2+(-625x)/750x^2+72x/750x^2-2=0

We multiply all the terms by the denominator


36x+(-625x)+72x-2*750x^2=0

We add all the numbers together, and all the variables

108x+(-625x)-2*750x^2=0

Wy multiply elements

-1500x^2+108x+(-625x)=0

We get rid of parentheses

-1500x^2+108x-625x=0

We add all the numbers together, and all the variables

-1500x^2-517x=0

a = -1500; b = -517; c = 0;
Δ = b2-4ac
Δ = -5172-4·(-1500)·0
Δ = 267289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{267289}=517$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-517)-517}{2*-1500}=\frac{0}{-3000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-517)+517}{2*-1500}=\frac{1034}{-3000}
=-517/1500
$