What are the solutions to the equation 5z^2-15z+11=0 ?

The solutions to the equation 5z^2-15z+11=0 are z=(15+sqrt(5))/(10),z=(15-sqrt(5))/(10)

Find the zeros of 5z^2-15z+11=0

The zeros of 5z^2-15z+11=0 are z=(15+sqrt(5))/(10),z=(15-sqrt(5))/(10)

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5 z^{2} - 15 z + 11 = 0

z = \frac{15 + 5}{10}, z = \frac{15 - 5}{10}

Decimal Notation

z = 1.72360 \dots, z = 1.27639 \dots

Solution steps

5 z^{2} - 15 z + 11 = 0

Solve with the quadratic formula

z_{1, 2} = \frac{- ( - 15 ) \pm ( - 15 ) ^{2} - 4 \cdot 5 \cdot 11}{2 \cdot 5}

(- 15)^{2} - 4 \cdot 5 \cdot 11 = 5

z_{1, 2} = \frac{- ( - 15 ) \pm 5}{2 \cdot 5}

Separate the solutions

z_{1} = \frac{- ( - 15 ) + 5}{2 \cdot 5}, z_{2} = \frac{- ( - 15 ) - 5}{2 \cdot 5}

z = \frac{- ( - 15 ) + 5}{2 \cdot 5} : \frac{15 + 5}{10}

z = \frac{- ( - 15 ) - 5}{2 \cdot 5} : \frac{15 - 5}{10}

The solutions to the quadratic equation are:

z = \frac{15 + 5}{10}, z = \frac{15 - 5}{10}

9 y^{2} + 25 = 30 y

x^{2} - 5 x + 25 = 4

x^{2} + 6 x - 3 = 12

3 m^{2} + 21 m - 8 = 0

4 x^{2} - 41 x = 73

What are the solutions to the equation 5z^2-15z+11=0 ?
The solutions to the equation 5z^2-15z+11=0 are z=(15+sqrt(5))/(10),z=(15-sqrt(5))/(10)
Find the zeros of 5z^2-15z+11=0
The zeros of 5z^2-15z+11=0 are z=(15+sqrt(5))/(10),z=(15-sqrt(5))/(10)