3/2x+x=24

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

3/2x+x=24

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x-24=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-48x+3=0

a = 2; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·2·3
Δ = 2280
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:

$\sqrt{\Delta}=\sqrt{2280}=\sqrt{4*570}=\sqrt{4}*\sqrt{570}=2\sqrt{570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{570}}{2*2}=\frac{48-2\sqrt{570}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{570}}{2*2}=\frac{48+2\sqrt{570}}{4}
$