3/22x+6=3x+9

Solution for 3/22x+6=3x+9 equation:

3/22x+6=3x+9

We move all terms to the left:

3/22x+6-(3x+9)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We get rid of parentheses

3/22x-3x-9+6=0

We multiply all the terms by the denominator


-3x*22x-9*22x+6*22x+3=0

Wy multiply elements

-66x^2-198x+132x+3=0

We add all the numbers together, and all the variables

-66x^2-66x+3=0

a = -66; b = -66; c = +3;
Δ = b2-4ac
Δ = -662-4·(-66)·3
Δ = 5148
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:

$\sqrt{\Delta}=\sqrt{5148}=\sqrt{36*143}=\sqrt{36}*\sqrt{143}=6\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{143}}{2*-66}=\frac{66-6\sqrt{143}}{-132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{143}}{2*-66}=\frac{66+6\sqrt{143}}{-132}
$