Solve X-2/3-X/(3-X)=2

Question

Solve the equation

X \in / R

Alternative Form

No real solution

Evaluate

X - \frac{2}{3} - \frac{X}{3 - X} = 2

Multiply both sides of the equation by LCD

(X - \frac{2}{3} - \frac{X}{3 - X}) \times 3 (3 - X) = 2 \times 3 (3 - X)

Simplify the equation

More Steps

8 X - 3 X^{2} - 6 = 2 \times 3 (3 - X)

Simplify the equation

More Steps

8 X - 3 X^{2} - 6 = 18 - 6 X

Move the expression to the left side

8 X - 3 X^{2} - 6 - (18 - 6 X) = 0

Subtract the terms

More Steps

14 X - 3 X^{2} - 24 = 0

Rewrite in standard form

- 3 X^{2} + 14 X - 24 = 0

Multiply both sides

3 X^{2} - 14 X + 24 = 0

Substitute a= 3,b= - 14 and c= 24 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 24}{2 \times 3}

Simplify the expression

X = \frac{14 \pm ( - 14 ) ^{2} - 4 \times 3 \times 24}{6}

Simplify the expression

More Steps

X = \frac{14 \pm - 92}{6}

Solution

X \in / R

Alternative Form

No real solution

Show Solution