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1x+2/3x=140
We move all terms to the left:
1x+2/3x-(140)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
x+2/3x-140=0
We multiply all the terms by the denominator
x*3x-140*3x+2=0
Wy multiply elements
3x^2-420x+2=0
a = 3; b = -420; c = +2;
Δ = b2-4ac
Δ = -4202-4·3·2
Δ = 176376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{176376}=\sqrt{4*44094}=\sqrt{4}*\sqrt{44094}=2\sqrt{44094}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44094}}{2*3}=\frac{420-2\sqrt{44094}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44094}}{2*3}=\frac{420+2\sqrt{44094}}{6} $
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