Solve 2(12g^2-g)=15

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

g_{1} = - \frac{3}{4}, g_{2} = \frac{5}{6}

Alternative Form

g_{1} = - 0.75, g_{2} = 0.8 \dot{3}

Evaluate

2 (12 g^{2} - g) = 15

Expand the expression

More Steps

Evaluate

2 (12 g^{2} - g)

Apply the distributive property

2 \times 12 g^{2} - 2 g

Multiply the numbers

24 g^{2} - 2 g

24 g^{2} - 2 g = 15

Move the expression to the left side

24 g^{2} - 2 g - 15 = 0

Factor the expression

More Steps

Evaluate

24 g^{2} - 2 g - 15

Rewrite the expression

24 g^{2} + (- 20 + 18) g - 15

Calculate

24 g^{2} - 20 g + 18 g - 15

Rewrite the expression

4 g \times 6 g - 4 g \times 5 + 3 \times 6 g - 3 \times 5

Factor out 4 g from the expression

4 g (6 g - 5) + 3 \times 6 g - 3 \times 5

Factor out 3 from the expression

4 g (6 g - 5) + 3 (6 g - 5)

Factor out 6 g - 5 from the expression

(4 g + 3) (6 g - 5)

(4 g + 3) (6 g - 5) = 0

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

6 g - 5 = 0 4 g + 3 = 0

Solve the equation for g

More Steps

Evaluate

6 g - 5 = 0

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

6 g = 0 + 5

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

6 g = 5

Divide both sides

\frac{6 g}{6} = \frac{5}{6}

Divide the numbers

g = \frac{5}{6}

g = \frac{5}{6} 4 g + 3 = 0

Solve the equation for g

More Steps

Evaluate

4 g + 3 = 0

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

4 g = 0 - 3

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

4 g = - 3

Divide both sides

\frac{4 g}{4} = \frac{- 3}{4}

Divide the numbers

g = \frac{- 3}{4}

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

g = - \frac{3}{4}

g = \frac{5}{6} g = - \frac{3}{4}

Solution

g_{1} = - \frac{3}{4}, g_{2} = \frac{5}{6}

Alternative Form

g_{1} = - 0.75, g_{2} = 0.8 \dot{3}

Show Solution