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66+57+1/2x+x=180
We move all terms to the left:
66+57+1/2x+x-(180)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
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} $
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