Solve 6x^2+7x-3=0

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} = \frac{1}{3}

Alternative Form

x_{1} = - 1.5, x_{2} = 0. \dot{3}

Evaluate

6 x^{2} + 7 x - 3 = 0

Factor the expression

More Steps

Evaluate

6 x^{2} + 7 x - 3

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out 2 x from the expression

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

Factor out 3 from the expression

2 x (3 x - 1) + 3 (3 x - 1)

Factor out 3 x - 1 from the expression

(2 x + 3) (3 x - 1)

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

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

3 x - 1 = 0 2 x + 3 = 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} 2 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 3 = 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 = \frac{1}{3} x = - \frac{3}{2}

Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = 0. \dot{3}

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