3(x+9)=5/4x

Solution for 3(x+9)=5/4x equation:

3(x+9)=5/4x

We move all terms to the left:

3(x+9)-(5/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(x+9)-(+5/4x)=0

We multiply parentheses

3x-(+5/4x)+27=0

We get rid of parentheses

3x-5/4x+27=0

We multiply all the terms by the denominator


3x*4x+27*4x-5=0

Wy multiply elements

12x^2+108x-5=0

a = 12; b = 108; c = -5;
Δ = b2-4ac
Δ = 1082-4·12·(-5)
Δ = 11904
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:

$\sqrt{\Delta}=\sqrt{11904}=\sqrt{64*186}=\sqrt{64}*\sqrt{186}=8\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-8\sqrt{186}}{2*12}=\frac{-108-8\sqrt{186}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+8\sqrt{186}}{2*12}=\frac{-108+8\sqrt{186}}{24}
$