-2x+9=1/3x-26

Solution for -2x+9=1/3x-26 equation:

-2x+9=1/3x-26

We move all terms to the left:

-2x+9-(1/3x-26)=0


Domain of the equation: 3x-26)!=0

x∈R


We get rid of parentheses

-2x-1/3x+26+9=0

We multiply all the terms by the denominator


-2x*3x+26*3x+9*3x-1=0

Wy multiply elements

-6x^2+78x+27x-1=0

We add all the numbers together, and all the variables

-6x^2+105x-1=0

a = -6; b = 105; c = -1;
Δ = b2-4ac
Δ = 1052-4·(-6)·(-1)
Δ = 11001
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{-(105)-\sqrt{11001}}{2*-6}=\frac{-105-\sqrt{11001}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11001}}{2*-6}=\frac{-105+\sqrt{11001}}{-12}
$