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x+(x-45)+(x-35)+1/2x=360
We move all terms to the left:
x+(x-45)+(x-35)+1/2x-(360)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
x+x+x+1/2x-45-35-360=0
We multiply all the terms by the denominator
x*2x+x*2x+x*2x-45*2x-35*2x-360*2x+1=0
Wy multiply elements
2x^2+2x^2+2x^2-90x-70x-720x+1=0
We add all the numbers together, and all the variables
6x^2-880x+1=0
a = 6; b = -880; c = +1;
Δ = b2-4ac
Δ = -8802-4·6·1
Δ = 774376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{774376}=\sqrt{4*193594}=\sqrt{4}*\sqrt{193594}=2\sqrt{193594}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-2\sqrt{193594}}{2*6}=\frac{880-2\sqrt{193594}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+2\sqrt{193594}}{2*6}=\frac{880+2\sqrt{193594}}{12} $
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