1/2x+3x=24-4x

Solution for 1/2x+3x=24-4x equation:

1/2x+3x=24-4x

We move all terms to the left:

1/2x+3x-(24-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+3x-(-4x+24)=0

We add all the numbers together, and all the variables

3x+1/2x-(-4x+24)=0

We get rid of parentheses

3x+1/2x+4x-24=0

We multiply all the terms by the denominator


3x*2x+4x*2x-24*2x+1=0

Wy multiply elements

6x^2+8x^2-48x+1=0

We add all the numbers together, and all the variables

14x^2-48x+1=0

a = 14; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·14·1
Δ = 2248
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:

$\sqrt{\Delta}=\sqrt{2248}=\sqrt{4*562}=\sqrt{4}*\sqrt{562}=2\sqrt{562}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{562}}{2*14}=\frac{48-2\sqrt{562}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{562}}{2*14}=\frac{48+2\sqrt{562}}{28}
$