X+(x+5)+1/2x=30

Solution for X+(x+5)+1/2x=30 equation:

X+(X+5)+1/2X=30

We move all terms to the left:

X+(X+5)+1/2X-(30)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

X+X+1/2X+5-30=0

We multiply all the terms by the denominator


X*2X+X*2X+5*2X-30*2X+1=0

Wy multiply elements

2X^2+2X^2+10X-60X+1=0

We add all the numbers together, and all the variables

4X^2-50X+1=0

a = 4; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·4·1
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{69}}{2*4}=\frac{50-6\sqrt{69}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{69}}{2*4}=\frac{50+6\sqrt{69}}{8}
$