4x-9+2/3x=21

Solution for 4x-9+2/3x=21 equation:

4x-9+2/3x=21

We move all terms to the left:

4x-9+2/3x-(21)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x+2/3x-30=0

We multiply all the terms by the denominator


4x*3x-30*3x+2=0

Wy multiply elements

12x^2-90x+2=0

a = 12; b = -90; c = +2;
Δ = b2-4ac
Δ = -902-4·12·2
Δ = 8004
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:

$\sqrt{\Delta}=\sqrt{8004}=\sqrt{4*2001}=\sqrt{4}*\sqrt{2001}=2\sqrt{2001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2001}}{2*12}=\frac{90-2\sqrt{2001}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2001}}{2*12}=\frac{90+2\sqrt{2001}}{24}
$