5/6x+1=-1/2x+9

Solution for 5/6x+1=-1/2x+9 equation:

5/6x+1=-1/2x+9

We move all terms to the left:

5/6x+1-(-1/2x+9)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

5/6x+1/2x-9+1=0

We calculate fractions


10x/12x^2+6x/12x^2-9+1=0

We add all the numbers together, and all the variables

10x/12x^2+6x/12x^2-8=0

We multiply all the terms by the denominator


10x+6x-8*12x^2=0

We add all the numbers together, and all the variables

16x-8*12x^2=0

Wy multiply elements

-96x^2+16x=0

a = -96; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-96)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-96}=\frac{-32}{-192}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-96}=\frac{0}{-192}
=0
$