What are the solutions to the equation 3v^2-18v-12=2 ?

The solutions to the equation 3v^2-18v-12=2 are v=(9+sqrt(123))/3 ,v=(9-sqrt(123))/3

Find the zeros of 3v^2-18v-12=2

The zeros of 3v^2-18v-12=2 are v=(9+sqrt(123))/3 ,v=(9-sqrt(123))/3

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3 v^{2} - 18 v - 12 = 2

v = \frac{9 + 123}{3}, v = \frac{9 - 123}{3}

Decimal Notation

v = 6.69684 \dots, v = - 0.69684 \dots

Solution steps

3 v^{2} - 18 v - 12 = 2

Move

2

to the left side

3 v^{2} - 18 v - 14 = 0

Solve with the quadratic formula

v_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 3 ( - 14 )}{2 \cdot 3}

(- 18)^{2} - 4 \cdot 3 (- 14) = 2123

v_{1, 2} = \frac{- ( - 18 ) \pm 2 123}{2 \cdot 3}

Separate the solutions

v_{1} = \frac{- ( - 18 ) + 2 123}{2 \cdot 3}, v_{2} = \frac{- ( - 18 ) - 2 123}{2 \cdot 3}

v = \frac{- ( - 18 ) + 2 123}{2 \cdot 3} : \frac{9 + 123}{3}

v = \frac{- ( - 18 ) - 2 123}{2 \cdot 3} : \frac{9 - 123}{3}

The solutions to the quadratic equation are:

v = \frac{9 + 123}{3}, v = \frac{9 - 123}{3}

0 = x^{2} + 5 x + 17

2 x^{2} + 3 x = 15 x

5 y^{2} - 7 = 25

x, z = 2 x^{2} + 2 y^{2} - 4

x^{2} - 5000.002 x + 10 = 0

What are the solutions to the equation 3v^2-18v-12=2 ?
The solutions to the equation 3v^2-18v-12=2 are v=(9+sqrt(123))/3 ,v=(9-sqrt(123))/3
Find the zeros of 3v^2-18v-12=2
The zeros of 3v^2-18v-12=2 are v=(9+sqrt(123))/3 ,v=(9-sqrt(123))/3