1/2x+65+x=180

Solution for 1/2x+65+x=180 equation:

1/2x+65+x=180

We move all terms to the left:

1/2x+65+x-(180)=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+1/2x-115=0

We multiply all the terms by the denominator


x*2x-115*2x+1=0

Wy multiply elements

2x^2-230x+1=0

a = 2; b = -230; c = +1;
Δ = b2-4ac
Δ = -2302-4·2·1
Δ = 52892
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:

$\sqrt{\Delta}=\sqrt{52892}=\sqrt{4*13223}=\sqrt{4}*\sqrt{13223}=2\sqrt{13223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-230)-2\sqrt{13223}}{2*2}=\frac{230-2\sqrt{13223}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-230)+2\sqrt{13223}}{2*2}=\frac{230+2\sqrt{13223}}{4}
$