What are the solutions to the equation -1/4 x^2-4/3 x+7=0 ?

The solutions to the equation -1/4 x^2-4/3 x+7=0 are x=-(2(4+sqrt(79)))/3 ,x=(2(sqrt(79)-4))/3

Find the zeros of -1/4 x^2-4/3 x+7=0

The zeros of -1/4 x^2-4/3 x+7=0 are x=-(2(4+sqrt(79)))/3 ,x=(2(sqrt(79)-4))/3

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- \frac{1}{4} x^{2} - \frac{4}{3} x + 7 = 0

x = - \frac{2 ( 4 + 79 )}{3}, x = \frac{2 ( 79 - 4 )}{3}

Decimal Notation

x = - 8.59212 \dots, x = 3.25879 \dots

Solution steps

- \frac{1}{4} x^{2} - \frac{4}{3} x + 7 = 0

Find Least Common Multiplier of

4, 3 : 12

Multiply by LCM=

12

- \frac{1}{4} x^{2} \cdot 12 - \frac{4}{3} x \cdot 12 + 7 \cdot 12 = 0 \cdot 12

Simplify

- 3 x^{2} - 16 x + 84 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 ( - 3 ) \cdot 84}{2 ( - 3 )}

(- 16)^{2} - 4 (- 3) \cdot 84 = 479

x_{1, 2} = \frac{- ( - 16 ) \pm 4 79}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - 16 ) + 4 79}{2 ( - 3 )}, x_{2} = \frac{- ( - 16 ) - 4 79}{2 ( - 3 )}

x = \frac{- ( - 16 ) + 4 79}{2 ( - 3 )} : - \frac{2 ( 4 + 79 )}{3}

x = \frac{- ( - 16 ) - 4 79}{2 ( - 3 )} : \frac{2 ( 79 - 4 )}{3}

The solutions to the quadratic equation are:

x = - \frac{2 ( 4 + 79 )}{3}, x = \frac{2 ( 79 - 4 )}{3}

(2 k + 2) x^{2} + (4 - 4 k) x + k - 2 = 0

2 d^{2} - 8 d + 19 = 6 d

12 x^{2} + 12 x - 6 = 0

2 x^{2} - 5 x = - 5

x^{2} - 5 x + 9 = 3

What are the solutions to the equation -1/4 x^2-4/3 x+7=0 ?
The solutions to the equation -1/4 x^2-4/3 x+7=0 are x=-(2(4+sqrt(79)))/3 ,x=(2(sqrt(79)-4))/3
Find the zeros of -1/4 x^2-4/3 x+7=0
The zeros of -1/4 x^2-4/3 x+7=0 are x=-(2(4+sqrt(79)))/3 ,x=(2(sqrt(79)-4))/3