What are the solutions to the equation (x^2)/2-(3x)/(20)= 1/5 ?

The solutions to the equation (x^2)/2-(3x)/(20)= 1/5 are x= 4/5 ,x=-1/2

Find the zeros of (x^2)/2-(3x)/(20)= 1/5

The zeros of (x^2)/2-(3x)/(20)= 1/5 are x= 4/5 ,x=-1/2

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\frac{x ^{2}}{2} - \frac{3 x}{20} = \frac{1}{5}

x = \frac{4}{5}, x = - \frac{1}{2}

Decimal Notation

x = 0.8, x = - 0.5

Solution steps

\frac{x ^{2}}{2} - \frac{3 x}{20} = \frac{1}{5}

Find Least Common Multiplier of

2, 20, 5 : 20

Multiply by LCM=

20

\frac{x ^{2}}{2} \cdot 20 - \frac{3 x}{20} \cdot 20 = \frac{1}{5} \cdot 20

Simplify

10 x^{2} - 3 x = 4

Move

4

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 10 ( - 4 )}{2 \cdot 10}

(- 3)^{2} - 4 \cdot 10 (- 4) = 13

x_{1, 2} = \frac{- ( - 3 ) \pm 13}{2 \cdot 10}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 13}{2 \cdot 10}, x_{2} = \frac{- ( - 3 ) - 13}{2 \cdot 10}

x = \frac{- ( - 3 ) + 13}{2 \cdot 10} : \frac{4}{5}

x = \frac{- ( - 3 ) - 13}{2 \cdot 10} : - \frac{1}{2}

The solutions to the quadratic equation are:

x = \frac{4}{5}, x = - \frac{1}{2}

∣ 5 x + 1 ∣ = ∣ 8 x + 4 ∣

3 x^{2} - 12 x - 9

∣ x - 4 ∣ < 1

\frac{x - 2}{6} \geq \frac{x - 1}{9} + \frac{7}{18}

- 15 x^{5} + 3 x

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