Solve 5-2x=3x^2 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{5}{3}, x_{2} = 1

Alternative Form

x_{1} = - 1. \dot{6}, x_{2} = 1

Evaluate

5 - 2 x = 3 x^{2}

Swap the sides

3 x^{2} = 5 - 2 x

Move the expression to the left side

3 x^{2} - 5 + 2 x = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 5 + 2 x

Reorder the terms

3 x^{2} + 2 x - 5

Rewrite the expression

3 x^{2} + (5 - 3) x - 5

Calculate

3 x^{2} + 5 x - 3 x - 5

Rewrite the expression

x \times 3 x + x \times 5 - 3 x - 5

Factor out x from the expression

x (3 x + 5) - 3 x - 5

Factor out - 1 from the expression

x (3 x + 5) - (3 x + 5)

Factor out 3 x + 5 from the expression

(x - 1) (3 x + 5)

(x - 1) (3 x + 5) = 0

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

x - 1 = 0 3 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 3 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 5 = 0

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

3 x = 0 - 5

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

3 x = - 5

Divide both sides

\frac{3 x}{3} = \frac{- 5}{3}

Divide the numbers

x = \frac{- 5}{3}

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

x = - \frac{5}{3}

x = 1 x = - \frac{5}{3}

Solution

x_{1} = - \frac{5}{3}, x_{2} = 1

Alternative Form

x_{1} = - 1. \dot{6}, x_{2} = 1

Show Solution