What are the solutions to the equation 2z^2-13z+3=-4z ?

The solutions to the equation 2z^2-13z+3=-4z are z=(9+sqrt(57))/4 ,z=(9-sqrt(57))/4

Find the zeros of 2z^2-13z+3=-4z

The zeros of 2z^2-13z+3=-4z are z=(9+sqrt(57))/4 ,z=(9-sqrt(57))/4

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2 z^{2} - 13 z + 3 = - 4 z

z = \frac{9 + 57}{4}, z = \frac{9 - 57}{4}

Decimal Notation

z = 4.13745 \dots, z = 0.36254 \dots

Solution steps

2 z^{2} - 13 z + 3 = - 4 z

Move

4 z

to the left side

2 z^{2} - 9 z + 3 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 2 \cdot 3}{2 \cdot 2}

(- 9)^{2} - 4 \cdot 2 \cdot 3 = 57

z_{1, 2} = \frac{- ( - 9 ) \pm 57}{2 \cdot 2}

Separate the solutions

z_{1} = \frac{- ( - 9 ) + 57}{2 \cdot 2}, z_{2} = \frac{- ( - 9 ) - 57}{2 \cdot 2}

z = \frac{- ( - 9 ) + 57}{2 \cdot 2} : \frac{9 + 57}{4}

z = \frac{- ( - 9 ) - 57}{2 \cdot 2} : \frac{9 - 57}{4}

The solutions to the quadratic equation are:

z = \frac{9 + 57}{4}, z = \frac{9 - 57}{4}

6 x + 6 (x - 5) = x (x - 5)

y^{2} - y - 14 = 2 y

\frac{1}{8} x^{2} + \frac{1}{4} x = 2

x^{2} - 17 x = - 10 x - 6

- 15 x^{2} = 0

What are the solutions to the equation 2z^2-13z+3=-4z ?
The solutions to the equation 2z^2-13z+3=-4z are z=(9+sqrt(57))/4 ,z=(9-sqrt(57))/4
Find the zeros of 2z^2-13z+3=-4z
The zeros of 2z^2-13z+3=-4z are z=(9+sqrt(57))/4 ,z=(9-sqrt(57))/4