What are the solutions to the equation 2.4z^2-7.4z-2.4=0 ?

The solutions to the equation 2.4z^2-7.4z-2.4=0 are z=(37+sqrt(1945))/(24),z=(37-sqrt(1945))/(24)

Find the zeros of 2.4z^2-7.4z-2.4=0

The zeros of 2.4z^2-7.4z-2.4=0 are z=(37+sqrt(1945))/(24),z=(37-sqrt(1945))/(24)

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2.4 z^{2} - 7.4 z - 2.4 = 0

z = \frac{37 + 1945}{24}, z = \frac{37 - 1945}{24}

Decimal Notation

z = 3.37925 \dots, z = - 0.29592 \dots

Solution steps

2.4 z^{2} - 7.4 z - 2.4 = 0

Multiply both sides by

10

24 z^{2} - 74 z - 24 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 74 ) \pm ( - 74 ) ^{2} - 4 \cdot 24 ( - 24 )}{2 \cdot 24}

(- 74)^{2} - 4 \cdot 24 (- 24) = 21945

z_{1, 2} = \frac{- ( - 74 ) \pm 2 1945}{2 \cdot 24}

Separate the solutions

z_{1} = \frac{- ( - 74 ) + 2 1945}{2 \cdot 24}, z_{2} = \frac{- ( - 74 ) - 2 1945}{2 \cdot 24}

z = \frac{- ( - 74 ) + 2 1945}{2 \cdot 24} : \frac{37 + 1945}{24}

z = \frac{- ( - 74 ) - 2 1945}{2 \cdot 24} : \frac{37 - 1945}{24}

The solutions to the quadratic equation are:

z = \frac{37 + 1945}{24}, z = \frac{37 - 1945}{24}

2 x^{2} + 4 x - 3 = 0

x^{2} + 4 x + 4 = - 25

x^{2} = - 5 x

x (x + 3) - 9 = 0

4 x^{2} + 16 x - 12 = 0

What are the solutions to the equation 2.4z^2-7.4z-2.4=0 ?
The solutions to the equation 2.4z^2-7.4z-2.4=0 are z=(37+sqrt(1945))/(24),z=(37-sqrt(1945))/(24)
Find the zeros of 2.4z^2-7.4z-2.4=0
The zeros of 2.4z^2-7.4z-2.4=0 are z=(37+sqrt(1945))/(24),z=(37-sqrt(1945))/(24)