Solve x x/2 - x/3 =2x-10

Evaluate

x \times \frac{x}{2} - \frac{x}{3} = 2 x - 10

Multiply the terms

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\frac{x ^{2}}{2} - \frac{x}{3} = 2 x - 10

Multiply both sides of the equation by LCD

(\frac{x ^{2}}{2} - \frac{x}{3}) \times 6 = (2 x - 10) \times 6

Simplify the equation

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3 x^{2} - 2 x = (2 x - 10) \times 6

Simplify the equation

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3 x^{2} - 2 x = 12 x - 60

Move the expression to the left side

3 x^{2} - 2 x - (12 x - 60) = 0

Subtract the terms

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3 x^{2} - 14 x + 60 = 0

Substitute a= 3,b= - 14 and c= 60 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{14 \pm ( - 14 ) ^{2} - 4 \times 3 \times 60}{2 \times 3}

Simplify the expression

x = \frac{14 \pm ( - 14 ) ^{2} - 4 \times 3 \times 60}{6}

Simplify the expression

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x = \frac{14 \pm - 524}{6}

Solution

x \in / R

Alternative Form

No real solution

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