What are the solutions to the equation 3x^2=7x+2 ?

The solutions to the equation 3x^2=7x+2 are x=(7+sqrt(73))/6 ,x=(7-sqrt(73))/6

Find the zeros of 3x^2=7x+2

The zeros of 3x^2=7x+2 are x=(7+sqrt(73))/6 ,x=(7-sqrt(73))/6

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3 x^{2} = 7 x + 2

x = \frac{7 + 73}{6}, x = \frac{7 - 73}{6}

Decimal Notation

x = 2.59066 \dots, x = - 0.25733 \dots

Solution steps

3 x^{2} = 7 x + 2

Move

2

to the left side

3 x^{2} - 2 = 7 x

Move

7 x

to the left side

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

Write in the standard form

a x^{2} + b x + c = 0

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 3 ( - 2 )}{2 \cdot 3}

(- 7)^{2} - 4 \cdot 3 (- 2) = 73

x_{1, 2} = \frac{- ( - 7 ) \pm 73}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 73}{2 \cdot 3}, x_{2} = \frac{- ( - 7 ) - 73}{2 \cdot 3}

x = \frac{- ( - 7 ) + 73}{2 \cdot 3} : \frac{7 + 73}{6}

x = \frac{- ( - 7 ) - 73}{2 \cdot 3} : \frac{7 - 73}{6}

The solutions to the quadratic equation are:

x = \frac{7 + 73}{6}, x = \frac{7 - 73}{6}

x - 8 = 15

\frac{5}{8} - \frac{1}{4}

3 b^{3} - 7 a b^{2} + 12 ab - 28 a^{2}

8 x^{2} + 13 x + 10 = 0

- 2 x^{2} + 144 = 0

What are the solutions to the equation 3x^2=7x+2 ?
The solutions to the equation 3x^2=7x+2 are x=(7+sqrt(73))/6 ,x=(7-sqrt(73))/6
Find the zeros of 3x^2=7x+2
The zeros of 3x^2=7x+2 are x=(7+sqrt(73))/6 ,x=(7-sqrt(73))/6