1/2x-9=13+6x

Solution for 1/2x-9=13+6x equation:

1/2x-9=13+6x

We move all terms to the left:

1/2x-9-(13+6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(6x+13)-9=0

We get rid of parentheses

1/2x-6x-13-9=0

We multiply all the terms by the denominator


-6x*2x-13*2x-9*2x+1=0

Wy multiply elements

-12x^2-26x-18x+1=0

We add all the numbers together, and all the variables

-12x^2-44x+1=0

a = -12; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·(-12)·1
Δ = 1984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{31}}{2*-12}=\frac{44-8\sqrt{31}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{31}}{2*-12}=\frac{44+8\sqrt{31}}{-24}
$