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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


25x/30x^2+12x/30x^2-1-2=0

We add all the numbers together, and all the variables

25x/30x^2+12x/30x^2-3=0

We multiply all the terms by the denominator


25x+12x-3*30x^2=0

We add all the numbers together, and all the variables

37x-3*30x^2=0

Wy multiply elements

-90x^2+37x=0

a = -90; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-90)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-90}=\frac{-74}{-180}
=37/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-90}=\frac{0}{-180}
=0
$