1/2(x)+9=180-x

Solution for 1/2(x)+9=180-x equation:

1/2(x)+9=180-x

We move all terms to the left:

1/2(x)+9-(180-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1x+180)+9=0

We get rid of parentheses

1/2x+1x-180+9=0

We multiply all the terms by the denominator


1x*2x-180*2x+9*2x+1=0

Wy multiply elements

2x^2-360x+18x+1=0

We add all the numbers together, and all the variables

2x^2-342x+1=0

a = 2; b = -342; c = +1;
Δ = b2-4ac
Δ = -3422-4·2·1
Δ = 116956
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:

$\sqrt{\Delta}=\sqrt{116956}=\sqrt{4*29239}=\sqrt{4}*\sqrt{29239}=2\sqrt{29239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-2\sqrt{29239}}{2*2}=\frac{342-2\sqrt{29239}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+2\sqrt{29239}}{2*2}=\frac{342+2\sqrt{29239}}{4}
$