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+21)!=0

x∈R


We get rid of parentheses

4x-2/3x-21-9=0

We multiply all the terms by the denominator


4x*3x-21*3x-9*3x-2=0

Wy multiply elements

12x^2-63x-27x-2=0

We add all the numbers together, and all the variables

12x^2-90x-2=0

a = 12; b = -90; c = -2;
Δ = b2-4ac
Δ = -902-4·12·(-2)
Δ = 8196
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:

$\sqrt{\Delta}=\sqrt{8196}=\sqrt{4*2049}=\sqrt{4}*\sqrt{2049}=2\sqrt{2049}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2049}}{2*12}=\frac{90-2\sqrt{2049}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2049}}{2*12}=\frac{90+2\sqrt{2049}}{24}
$