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

The solutions to the equation 3a^2-a+2=7a are a=(4+sqrt(10))/3 ,a=(4-sqrt(10))/3

Find the zeros of 3a^2-a+2=7a

The zeros of 3a^2-a+2=7a are a=(4+sqrt(10))/3 ,a=(4-sqrt(10))/3

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3 a^{2} - a + 2 = 7 a

a = \frac{4 + 10}{3}, a = \frac{4 - 10}{3}

Decimal Notation

a = 2.38742 \dots, a = 0.27924 \dots

Solution steps

3 a^{2} - a + 2 = 7 a

Move

7 a

to the left side

3 a^{2} - 8 a + 2 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 3 \cdot 2}{2 \cdot 3}

(- 8)^{2} - 4 \cdot 3 \cdot 2 = 210

a_{1, 2} = \frac{- ( - 8 ) \pm 2 10}{2 \cdot 3}

Separate the solutions

a_{1} = \frac{- ( - 8 ) + 2 10}{2 \cdot 3}, a_{2} = \frac{- ( - 8 ) - 2 10}{2 \cdot 3}

a = \frac{- ( - 8 ) + 2 10}{2 \cdot 3} : \frac{4 + 10}{3}

a = \frac{- ( - 8 ) - 2 10}{2 \cdot 3} : \frac{4 - 10}{3}

The solutions to the quadratic equation are:

a = \frac{4 + 10}{3}, a = \frac{4 - 10}{3}

x, y = a x^{2} + b x + c

x^{2} - 16 x - 38 = 0

x^{2} + 4 x - 5

x, x^{2} + 3 y^{2} - 4 x + 24 y + 52 = 0

s^{2} + 4 s + 1 = 0

What are the solutions to the equation 3a^2-a+2=7a ?
The solutions to the equation 3a^2-a+2=7a are a=(4+sqrt(10))/3 ,a=(4-sqrt(10))/3
Find the zeros of 3a^2-a+2=7a
The zeros of 3a^2-a+2=7a are a=(4+sqrt(10))/3 ,a=(4-sqrt(10))/3