2/3x-9=13x

Solution for 2/3x-9=13x equation:

2/3x-9=13x

We move all terms to the left:

2/3x-9-(13x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-13x+2/3x-9=0

We multiply all the terms by the denominator


-13x*3x-9*3x+2=0

Wy multiply elements

-39x^2-27x+2=0

a = -39; b = -27; c = +2;
Δ = b2-4ac
Δ = -272-4·(-39)·2
Δ = 1041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{1041}}{2*-39}=\frac{27-\sqrt{1041}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1041}}{2*-39}=\frac{27+\sqrt{1041}}{-78}
$