5/2x+x-5+x=67

Solution for 5/2x+x-5+x=67 equation:

5/2x+x-5+x=67

We move all terms to the left:

5/2x+x-5+x-(67)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+5/2x-72=0

We multiply all the terms by the denominator


2x*2x-72*2x+5=0

Wy multiply elements

4x^2-144x+5=0

a = 4; b = -144; c = +5;
Δ = b2-4ac
Δ = -1442-4·4·5
Δ = 20656
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:

$\sqrt{\Delta}=\sqrt{20656}=\sqrt{16*1291}=\sqrt{16}*\sqrt{1291}=4\sqrt{1291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1291}}{2*4}=\frac{144-4\sqrt{1291}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1291}}{2*4}=\frac{144+4\sqrt{1291}}{8}
$