90-x=1/3x

Solution for 90-x=1/3x equation:

90-x=1/3x

We move all terms to the left:

90-x-(1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+1/3x)+90=0

We add all the numbers together, and all the variables

-1x-(+1/3x)+90=0

We get rid of parentheses

-1x-1/3x+90=0

We multiply all the terms by the denominator


-1x*3x+90*3x-1=0

Wy multiply elements

-3x^2+270x-1=0

a = -3; b = 270; c = -1;
Δ = b2-4ac
Δ = 2702-4·(-3)·(-1)
Δ = 72888
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:

$\sqrt{\Delta}=\sqrt{72888}=\sqrt{4*18222}=\sqrt{4}*\sqrt{18222}=2\sqrt{18222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-2\sqrt{18222}}{2*-3}=\frac{-270-2\sqrt{18222}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+2\sqrt{18222}}{2*-3}=\frac{-270+2\sqrt{18222}}{-6}
$