2x-6=4/9x+8

Solution for 2x-6=4/9x+8 equation:

2x-6=4/9x+8

We move all terms to the left:

2x-6-(4/9x+8)=0


Domain of the equation: 9x+8)!=0

x∈R


We get rid of parentheses

2x-4/9x-8-6=0

We multiply all the terms by the denominator


2x*9x-8*9x-6*9x-4=0

Wy multiply elements

18x^2-72x-54x-4=0

We add all the numbers together, and all the variables

18x^2-126x-4=0

a = 18; b = -126; c = -4;
Δ = b2-4ac
Δ = -1262-4·18·(-4)
Δ = 16164
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:

$\sqrt{\Delta}=\sqrt{16164}=\sqrt{36*449}=\sqrt{36}*\sqrt{449}=6\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-6\sqrt{449}}{2*18}=\frac{126-6\sqrt{449}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+6\sqrt{449}}{2*18}=\frac{126+6\sqrt{449}}{36}
$