x-32=1/3x+99

Solution for x-32=1/3x+99 equation:

x-32=1/3x+99

We move all terms to the left:

x-32-(1/3x+99)=0


Domain of the equation: 3x+99)!=0

x∈R


We get rid of parentheses

x-1/3x-99-32=0

We multiply all the terms by the denominator


x*3x-99*3x-32*3x-1=0

Wy multiply elements

3x^2-297x-96x-1=0

We add all the numbers together, and all the variables

3x^2-393x-1=0

a = 3; b = -393; c = -1;
Δ = b2-4ac
Δ = -3932-4·3·(-1)
Δ = 154461
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{-(-393)-\sqrt{154461}}{2*3}=\frac{393-\sqrt{154461}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-393)+\sqrt{154461}}{2*3}=\frac{393+\sqrt{154461}}{6}
$