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

Solution for 2^1/2x-5/6x-2=0 equation:

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


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

Fractions to decimals

(-10x)/12x^2-2+1=0

We multiply all the terms by the denominator


(-10x)-2*12x^2+1*12x^2=0

Wy multiply elements

-24x^2+12x^2+(-10x)=0

We get rid of parentheses

-24x^2+12x^2-10x=0

We add all the numbers together, and all the variables

-12x^2-10x=0

a = -12; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-12)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-12}=\frac{20}{-24}
=-5/6
$