(1/2)x+(x-5)+x=180

Solution for (1/2)x+(x-5)+x=180 equation:

(1/2)x+(x-5)+x=180

We move all terms to the left:

(1/2)x+(x-5)+x-(180)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x+(x-5)+x-180=0

We add all the numbers together, and all the variables

x+(+1/2)x+(x-5)-180=0

We multiply parentheses

x^2+x+(x-5)-180=0

We get rid of parentheses

x^2+x+x-5-180=0

We add all the numbers together, and all the variables

x^2+2x-185=0

a = 1; b = 2; c = -185;
Δ = b2-4ac
Δ = 22-4·1·(-185)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{186}}{2*1}=\frac{-2-2\sqrt{186}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{186}}{2*1}=\frac{-2+2\sqrt{186}}{2}
$