What are the solutions to the equation 1/2 u^2+3/4 u=-1/5 ?

The solutions to the equation 1/2 u^2+3/4 u=-1/5 are u=(-15+sqrt(65))/(20),u=(-15-sqrt(65))/(20)

Find the zeros of 1/2 u^2+3/4 u=-1/5

The zeros of 1/2 u^2+3/4 u=-1/5 are u=(-15+sqrt(65))/(20),u=(-15-sqrt(65))/(20)

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\frac{1}{2} u^{2} + \frac{3}{4} u = - \frac{1}{5}

u = \frac{- 15 + 65}{20}, u = \frac{- 15 - 65}{20}

Decimal Notation

u = - 0.34688 \dots, u = - 1.15311 \dots

Solution steps

\frac{1}{2} u^{2} + \frac{3}{4} u = - \frac{1}{5}

Find Least Common Multiplier of

2, 4, 5 : 20

Multiply by LCM=

20

\frac{1}{2} u^{2} \cdot 20 + \frac{3}{4} u \cdot 20 = - \frac{1}{5} \cdot 20

Simplify

10 u^{2} + 15 u = - 4

Move

4

to the left side

10 u^{2} + 15 u + 4 = 0

Solve with the quadratic formula

u_{1, 2} = \frac{- 15 \pm 1 5 ^{2} - 4 \cdot 10 \cdot 4}{2 \cdot 10}

1 5^{2} - 4 \cdot 10 \cdot 4 = 65

u_{1, 2} = \frac{- 15 \pm 65}{2 \cdot 10}

Separate the solutions

u_{1} = \frac{- 15 + 65}{2 \cdot 10}, u_{2} = \frac{- 15 - 65}{2 \cdot 10}

u = \frac{- 15 + 65}{2 \cdot 10} : \frac{- 15 + 65}{20}

u = \frac{- 15 - 65}{2 \cdot 10} : \frac{- 15 - 65}{20}

The solutions to the quadratic equation are:

u = \frac{- 15 + 65}{20}, u = \frac{- 15 - 65}{20}

x + x^{2} = 42

a, b^{2} x^{2} - a^{2} y^{2} = a^{2} b^{2}

x^{2} - a^{2} = 0

x^{2} = 1 2^{2} + 9^{2}

4 x^{2} = - 10 x + 14

What are the solutions to the equation 1/2 u^2+3/4 u=-1/5 ?
The solutions to the equation 1/2 u^2+3/4 u=-1/5 are u=(-15+sqrt(65))/(20),u=(-15-sqrt(65))/(20)
Find the zeros of 1/2 u^2+3/4 u=-1/5
The zeros of 1/2 u^2+3/4 u=-1/5 are u=(-15+sqrt(65))/(20),u=(-15-sqrt(65))/(20)