6(x+2)=5/4x

Solution for 6(x+2)=5/4x equation:

6(x+2)=5/4x

We move all terms to the left:

6(x+2)-(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

6(x+2)-(+5/4x)=0

We multiply parentheses

6x-(+5/4x)+12=0

We get rid of parentheses

6x-5/4x+12=0

We multiply all the terms by the denominator


6x*4x+12*4x-5=0

Wy multiply elements

24x^2+48x-5=0

a = 24; b = 48; c = -5;
Δ = b2-4ac
Δ = 482-4·24·(-5)
Δ = 2784
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:

$\sqrt{\Delta}=\sqrt{2784}=\sqrt{16*174}=\sqrt{16}*\sqrt{174}=4\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{174}}{2*24}=\frac{-48-4\sqrt{174}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{174}}{2*24}=\frac{-48+4\sqrt{174}}{48}
$