3/4x=24+x

Solution for 3/4x=24+x equation:

3/4x=24+x

We move all terms to the left:

3/4x-(24+x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(x+24)=0

We get rid of parentheses

3/4x-x-24=0

We multiply all the terms by the denominator


-x*4x-24*4x+3=0

Wy multiply elements

-4x^2-96x+3=0

a = -4; b = -96; c = +3;
Δ = b2-4ac
Δ = -962-4·(-4)·3
Δ = 9264
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:

$\sqrt{\Delta}=\sqrt{9264}=\sqrt{16*579}=\sqrt{16}*\sqrt{579}=4\sqrt{579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{579}}{2*-4}=\frac{96-4\sqrt{579}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{579}}{2*-4}=\frac{96+4\sqrt{579}}{-8}
$