3(x-4)=5/2x

Solution for 3(x-4)=5/2x equation:

3(x-4)=5/2x

We move all terms to the left:

3(x-4)-(5/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3x-(+5/2x)-12=0

We get rid of parentheses

3x-5/2x-12=0

We multiply all the terms by the denominator


3x*2x-12*2x-5=0

Wy multiply elements

6x^2-24x-5=0

a = 6; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·6·(-5)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{174}}{2*6}=\frac{24-2\sqrt{174}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{174}}{2*6}=\frac{24+2\sqrt{174}}{12}
$