Solve 6-3x=15-2(x^2)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{3}{2}, x_{2} = 3

Alternative Form

x_{1} = - 1.5, x_{2} = 3

Evaluate

6 - 3 x = 15 - 2 x^{2}

Swap the sides

15 - 2 x^{2} = 6 - 3 x

Move the expression to the left side

9 - 2 x^{2} + 3 x = 0

Factor the expression

More Steps

Evaluate

9 - 2 x^{2} + 3 x

Reorder the terms

9 + 3 x - 2 x^{2}

Rewrite the expression

9 + (6 - 3) x - 2 x^{2}

Calculate

9 + 6 x - 3 x - 2 x^{2}

Rewrite the expression

3 \times 3 + 3 \times 2 x - x \times 3 - x \times 2 x

Factor out 3 from the expression

3 (3 + 2 x) - x \times 3 - x \times 2 x

Factor out - x from the expression

3 (3 + 2 x) - x (3 + 2 x)

Factor out 3 + 2 x from the expression

(3 - x) (3 + 2 x)

(3 - x) (3 + 2 x) = 0

When the product of factors equals 0,at least one factor is 0

3 - x = 0 3 + 2 x = 0

Solve the equation for x

More Steps

Evaluate

3 - x = 0

Move the constant to the right-hand side and change its sign

- x = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

- x = - 3

Change the signs on both sides of the equation

x = 3

x = 3 3 + 2 x = 0

Solve the equation for x

More Steps

Evaluate

3 + 2 x = 0

Move the constant to the right-hand side and change its sign

2 x = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

2 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{3}{2}

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

Solution

x_{1} = - \frac{3}{2}, x_{2} = 3

Alternative Form

x_{1} = - 1.5, x_{2} = 3

Show Solution