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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2-39x=0

a = 6; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·6·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*6}=\frac{78}{12}
=6+1/2
$