-1/3x+5=2x+9

Solution for -1/3x+5=2x+9 equation:

-1/3x+5=2x+9

We move all terms to the left:

-1/3x+5-(2x+9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x-2x-9+5=0

We multiply all the terms by the denominator


-2x*3x-9*3x+5*3x-1=0

Wy multiply elements

-6x^2-27x+15x-1=0

We add all the numbers together, and all the variables

-6x^2-12x-1=0

a = -6; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-6)·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-6}=\frac{12-2\sqrt{30}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-6}=\frac{12+2\sqrt{30}}{-12}
$