2/3x-6+x+21=90

Solution for 2/3x-6+x+21=90 equation:

2/3x-6+x+21=90

We move all terms to the left:

2/3x-6+x+21-(90)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/3x-75=0

We multiply all the terms by the denominator


x*3x-75*3x+2=0

Wy multiply elements

3x^2-225x+2=0

a = 3; b = -225; c = +2;
Δ = b2-4ac
Δ = -2252-4·3·2
Δ = 50601
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{-(-225)-\sqrt{50601}}{2*3}=\frac{225-\sqrt{50601}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+\sqrt{50601}}{2*3}=\frac{225+\sqrt{50601}}{6}
$