1/2x-5/6x=10

Solution for 1/2x-5/6x=10 equation:

1/2x-5/6x=10

We move all terms to the left:

1/2x-5/6x-(10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


6x/12x^2+(-10x)/12x^2-10=0

We multiply all the terms by the denominator


6x+(-10x)-10*12x^2=0

Wy multiply elements

-120x^2+6x+(-10x)=0

We get rid of parentheses

-120x^2+6x-10x=0

We add all the numbers together, and all the variables

-120x^2-4x=0

a = -120; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-120)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-120}=\frac{8}{-240}
=-1/30
$