What are the solutions to the equation (x^2)/5-x/2 = 4/5 ?

The solutions to the equation (x^2)/5-x/2 = 4/5 are x=(5+sqrt(89))/4 ,x=(5-sqrt(89))/4

Find the zeros of (x^2)/5-x/2 = 4/5

The zeros of (x^2)/5-x/2 = 4/5 are x=(5+sqrt(89))/4 ,x=(5-sqrt(89))/4

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\frac{x ^{2}}{5} - \frac{x}{2} = \frac{4}{5}

x = \frac{5 + 89}{4}, x = \frac{5 - 89}{4}

Decimal Notation

x = 3.60849 \dots, x = - 1.10849 \dots

Solution steps

\frac{x ^{2}}{5} - \frac{x}{2} = \frac{4}{5}

Find Least Common Multiplier of

5, 2 : 10

Multiply by LCM=

10

\frac{x ^{2}}{5} \cdot 10 - \frac{x}{2} \cdot 10 = \frac{4}{5} \cdot 10

Simplify

2 x^{2} - 5 x = 8

Move

8

to the left side

2 x^{2} - 5 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 2 ( - 8 )}{2 \cdot 2}

(- 5)^{2} - 4 \cdot 2 (- 8) = 89

x_{1, 2} = \frac{- ( - 5 ) \pm 89}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 89}{2 \cdot 2}, x_{2} = \frac{- ( - 5 ) - 89}{2 \cdot 2}

x = \frac{- ( - 5 ) + 89}{2 \cdot 2} : \frac{5 + 89}{4}

x = \frac{- ( - 5 ) - 89}{2 \cdot 2} : \frac{5 - 89}{4}

The solutions to the quadratic equation are:

x = \frac{5 + 89}{4}, x = \frac{5 - 89}{4}

y^{2} + 1 = \frac{y + 8}{2}

20 x^{2} + 13 x - 15 = 0

3 5^{2} = 6^{2} + x^{2}

f, (f)^{2} + g = x y - 1

x^{2} + 15 x + 26 = 0

What are the solutions to the equation (x^2)/5-x/2 = 4/5 ?
The solutions to the equation (x^2)/5-x/2 = 4/5 are x=(5+sqrt(89))/4 ,x=(5-sqrt(89))/4
Find the zeros of (x^2)/5-x/2 = 4/5
The zeros of (x^2)/5-x/2 = 4/5 are x=(5+sqrt(89))/4 ,x=(5-sqrt(89))/4