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1/3x+30x+40=360
We move all terms to the left:
1/3x+30x+40-(360)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
30x+1/3x-320=0
We multiply all the terms by the denominator
30x*3x-320*3x+1=0
Wy multiply elements
90x^2-960x+1=0
a = 90; b = -960; c = +1;
Δ = b2-4ac
Δ = -9602-4·90·1
Δ = 921240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{921240}=\sqrt{36*25590}=\sqrt{36}*\sqrt{25590}=6\sqrt{25590}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-6\sqrt{25590}}{2*90}=\frac{960-6\sqrt{25590}}{180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+6\sqrt{25590}}{2*90}=\frac{960+6\sqrt{25590}}{180} $
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