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x-60=2/3x

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Solution for x-60=2/3x equation:



x-60=2/3x
We move all terms to the left:
x-60-(2/3x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(+2/3x)-60=0
We get rid of parentheses
x-2/3x-60=0
We multiply all the terms by the denominator
x*3x-60*3x-2=0
Wy multiply elements
3x^2-180x-2=0
a = 3; b = -180; c = -2;
Δ = b2-4ac
Δ = -1802-4·3·(-2)
Δ = 32424
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{32424}=\sqrt{4*8106}=\sqrt{4}*\sqrt{8106}=2\sqrt{8106}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8106}}{2*3}=\frac{180-2\sqrt{8106}}{6}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8106}}{2*3}=\frac{180+2\sqrt{8106}}{6}

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