What are the solutions to the equation 2z^2-5z-2=-3z^2 ?

The solutions to the equation 2z^2-5z-2=-3z^2 are z=(5+sqrt(65))/(10),z=(5-sqrt(65))/(10)

Find the zeros of 2z^2-5z-2=-3z^2

The zeros of 2z^2-5z-2=-3z^2 are z=(5+sqrt(65))/(10),z=(5-sqrt(65))/(10)

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2 z^{2} - 5 z - 2 = - 3 z^{2}

z = \frac{5 + 65}{10}, z = \frac{5 - 65}{10}

Decimal Notation

z = 1.30622 \dots, z = - 0.30622 \dots

Solution steps

2 z^{2} - 5 z - 2 = - 3 z^{2}

Move

3 z^{2}

to the left side

5 z^{2} - 5 z - 2 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 5 ( - 2 )}{2 \cdot 5}

(- 5)^{2} - 4 \cdot 5 (- 2) = 65

z_{1, 2} = \frac{- ( - 5 ) \pm 65}{2 \cdot 5}

Separate the solutions

z_{1} = \frac{- ( - 5 ) + 65}{2 \cdot 5}, z_{2} = \frac{- ( - 5 ) - 65}{2 \cdot 5}

z = \frac{- ( - 5 ) + 65}{2 \cdot 5} : \frac{5 + 65}{10}

z = \frac{- ( - 5 ) - 65}{2 \cdot 5} : \frac{5 - 65}{10}

The solutions to the quadratic equation are:

z = \frac{5 + 65}{10}, z = \frac{5 - 65}{10}

15 x^{2} - 11 x - 12 = 0

(x - 2) (x - 3) = 20

(3 - x)^{2} = 0

3 x^{2} - 104 = - 8

12 - x^{2} - x = 2 x^{2} - 4 x + 6

What are the solutions to the equation 2z^2-5z-2=-3z^2 ?
The solutions to the equation 2z^2-5z-2=-3z^2 are z=(5+sqrt(65))/(10),z=(5-sqrt(65))/(10)
Find the zeros of 2z^2-5z-2=-3z^2
The zeros of 2z^2-5z-2=-3z^2 are z=(5+sqrt(65))/(10),z=(5-sqrt(65))/(10)