(x+3)+1/2x=24

Solution for (x+3)+1/2x=24 equation:

(x+3)+1/2x=24

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2-42x+1=0

a = 2; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·2·1
Δ = 1756
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:

$\sqrt{\Delta}=\sqrt{1756}=\sqrt{4*439}=\sqrt{4}*\sqrt{439}=2\sqrt{439}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{439}}{2*2}=\frac{42-2\sqrt{439}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{439}}{2*2}=\frac{42+2\sqrt{439}}{4}
$