8(x-3)=1/324x-72

Solution for 8(x-3)=1/324x-72 equation:

8(x-3)=1/324x-72

We move all terms to the left:

8(x-3)-(1/324x-72)=0


Domain of the equation: 324x-72)!=0

x∈R


We multiply parentheses

8x-(1/324x-72)-24=0

We get rid of parentheses

8x-1/324x+72-24=0

We multiply all the terms by the denominator


8x*324x+72*324x-24*324x-1=0

Wy multiply elements

2592x^2+23328x-7776x-1=0

We add all the numbers together, and all the variables

2592x^2+15552x-1=0

a = 2592; b = 15552; c = -1;
Δ = b2-4ac
Δ = 155522-4·2592·(-1)
Δ = 241875072
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:

$\sqrt{\Delta}=\sqrt{241875072}=\sqrt{5184*46658}=\sqrt{5184}*\sqrt{46658}=72\sqrt{46658}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15552)-72\sqrt{46658}}{2*2592}=\frac{-15552-72\sqrt{46658}}{5184}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15552)+72\sqrt{46658}}{2*2592}=\frac{-15552+72\sqrt{46658}}{5184}
$