Solve 6(-2g-1)=-(13g^2)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

g_{1} = \frac{6 - 114}{13}, g_{2} = \frac{6 + 114}{13}

Alternative Form

g_{1} \approx - 0.359775, g_{2} \approx 1.282852

Evaluate

6 (- 2 g - 1) = - 13 g^{2}

Swap the sides

- 13 g^{2} = 6 (- 2 g - 1)

Expand the expression

More Steps

- 13 g^{2} = - 12 g - 6

Move the expression to the left side

- 13 g^{2} + 12 g + 6 = 0

Multiply both sides

13 g^{2} - 12 g - 6 = 0

Substitute a= 13,b= - 12 and c= - 6 into the quadratic formula g = \frac{- b \pm b ^{2} - 4 a c}{2 a}

g = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 13 ( - 6 )}{2 \times 13}

Simplify the expression

g = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 13 ( - 6 )}{26}

Simplify the expression

More Steps

g = \frac{12 \pm 456}{26}

Simplify the radical expression

More Steps

g = \frac{12 \pm 2 114}{26}

Separate the equation into 2 possible cases

g = \frac{12 + 2 114}{26} g = \frac{12 - 2 114}{26}

Simplify the expression

More Steps

g = \frac{6 + 114}{13} g = \frac{12 - 2 114}{26}

Simplify the expression

More Steps

g = \frac{6 + 114}{13} g = \frac{6 - 114}{13}

Solution

g_{1} = \frac{6 - 114}{13}, g_{2} = \frac{6 + 114}{13}

Alternative Form

g_{1} \approx - 0.359775, g_{2} \approx 1.282852

Show Solution