2/3x=90-x

Solution for 2/3x=90-x equation:

2/3x=90-x

We move all terms to the left:

2/3x-(90-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1x+90)=0

We get rid of parentheses

2/3x+1x-90=0

We multiply all the terms by the denominator


1x*3x-90*3x+2=0

Wy multiply elements

3x^2-270x+2=0

a = 3; b = -270; c = +2;
Δ = b2-4ac
Δ = -2702-4·3·2
Δ = 72876
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:

$\sqrt{\Delta}=\sqrt{72876}=\sqrt{4*18219}=\sqrt{4}*\sqrt{18219}=2\sqrt{18219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18219}}{2*3}=\frac{270-2\sqrt{18219}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18219}}{2*3}=\frac{270+2\sqrt{18219}}{6}
$