Solve 3x^2 +20x-5=6x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 5, x_{2} = 0. \dot{3}

Evaluate

3 x^{2} + 20 x - 5 = 6 x

Move the expression to the left side

3 x^{2} + 14 x - 5 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} + 14 x - 5

Rewrite the expression

3 x^{2} + (- 1 + 15) x - 5

Calculate

3 x^{2} - x + 15 x - 5

Rewrite the expression

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

Factor out x from the expression

x (3 x - 1) + 5 \times 3 x - 5

Factor out 5 from the expression

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

Factor out 3 x - 1 from the expression

(x + 5) (3 x - 1)

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

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

3 x - 1 = 0 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 1 = 0

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

3 x = 0 + 1

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

3 x = 1

Divide both sides

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

Divide the numbers

x = \frac{1}{3}

x = \frac{1}{3} x + 5 = 0

Solve the equation for x

More Steps

Evaluate

x + 5 = 0

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

x = 0 - 5

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

x = - 5

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

Solution

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

Alternative Form

x_{1} = - 5, x_{2} = 0. \dot{3}

Show Solution