1/3x-9=x-29

Solution for 1/3x-9=x-29 equation:

1/3x-9=x-29

We move all terms to the left:

1/3x-9-(x-29)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+29-9=0

We multiply all the terms by the denominator


-x*3x+29*3x-9*3x+1=0

Wy multiply elements

-3x^2+87x-27x+1=0

We add all the numbers together, and all the variables

-3x^2+60x+1=0

a = -3; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-3)·1
Δ = 3612
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:

$\sqrt{\Delta}=\sqrt{3612}=\sqrt{4*903}=\sqrt{4}*\sqrt{903}=2\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{903}}{2*-3}=\frac{-60-2\sqrt{903}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{903}}{2*-3}=\frac{-60+2\sqrt{903}}{-6}
$