66+(1/2x+57)+x=180

Solution for 66+(1/2x+57)+x=180 equation:

66+(1/2x+57)+x=180

We move all terms to the left:

66+(1/2x+57)+x-(180)=0


Domain of the equation: 2x+57)!=0

x∈R


We add all the numbers together, and all the variables

x+(1/2x+57)-114=0

We get rid of parentheses

x+1/2x+57-114=0

We multiply all the terms by the denominator


x*2x+57*2x-114*2x+1=0

Wy multiply elements

2x^2+114x-228x+1=0

We add all the numbers together, and all the variables

2x^2-114x+1=0

a = 2; b = -114; c = +1;
Δ = b2-4ac
Δ = -1142-4·2·1
Δ = 12988
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:

$\sqrt{\Delta}=\sqrt{12988}=\sqrt{4*3247}=\sqrt{4}*\sqrt{3247}=2\sqrt{3247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3247}}{2*2}=\frac{114-2\sqrt{3247}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3247}}{2*2}=\frac{114+2\sqrt{3247}}{4}
$