(x+3)+x+1/2x=33

Solution for (x+3)+x+1/2x=33 equation:

(x+3)+x+1/2x=33

We move all terms to the left:

(x+3)+x+1/2x-(33)=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+(x+3)+1/2x-33=0

We get rid of parentheses

x+x+1/2x+3-33=0

We multiply all the terms by the denominator


x*2x+x*2x+3*2x-33*2x+1=0

Wy multiply elements

2x^2+2x^2+6x-66x+1=0

We add all the numbers together, and all the variables

4x^2-60x+1=0

a = 4; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·4·1
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{14}}{2*4}=\frac{60-16\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{14}}{2*4}=\frac{60+16\sqrt{14}}{8}
$