3x+24=7/2x

Solution for 3x+24=7/2x equation:

3x+24=7/2x

We move all terms to the left:

3x+24-(7/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+7/2x)+24=0

We get rid of parentheses

3x-7/2x+24=0

We multiply all the terms by the denominator


3x*2x+24*2x-7=0

Wy multiply elements

6x^2+48x-7=0

a = 6; b = 48; c = -7;
Δ = b2-4ac
Δ = 482-4·6·(-7)
Δ = 2472
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:

$\sqrt{\Delta}=\sqrt{2472}=\sqrt{4*618}=\sqrt{4}*\sqrt{618}=2\sqrt{618}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{618}}{2*6}=\frac{-48-2\sqrt{618}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{618}}{2*6}=\frac{-48+2\sqrt{618}}{12}
$