1/2x+51+x=180

Solution for 1/2x+51+x=180 equation:

1/2x+51+x=180

We move all terms to the left:

1/2x+51+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-129=0

We multiply all the terms by the denominator


x*2x-129*2x+1=0

Wy multiply elements

2x^2-258x+1=0

a = 2; b = -258; c = +1;
Δ = b2-4ac
Δ = -2582-4·2·1
Δ = 66556
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:

$\sqrt{\Delta}=\sqrt{66556}=\sqrt{4*16639}=\sqrt{4}*\sqrt{16639}=2\sqrt{16639}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-258)-2\sqrt{16639}}{2*2}=\frac{258-2\sqrt{16639}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-258)+2\sqrt{16639}}{2*2}=\frac{258+2\sqrt{16639}}{4}
$