66+X+57+1/2x=180

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

66+X+57+1/2X=180

We move all terms to the left:

66+X+57+1/2X-(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-57=0

We multiply all the terms by the denominator


X*2X-57*2X+1=0

Wy multiply elements

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}
$