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2/3x+x=20

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Solution for 2/3x+x=20 equation:



2/3x+x=20
We move all terms to the left:
2/3x+x-(20)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
x+2/3x-20=0
We multiply all the terms by the denominator
x*3x-20*3x+2=0
Wy multiply elements
3x^2-60x+2=0
a = 3; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·3·2
Δ = 3576
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{3576}=\sqrt{4*894}=\sqrt{4}*\sqrt{894}=2\sqrt{894}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{894}}{2*3}=\frac{60-2\sqrt{894}}{6}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{894}}{2*3}=\frac{60+2\sqrt{894}}{6}

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