What are the solutions to the equation (x^2)/4+1/10 =(x^2)/5+x/2 ?

The solutions to the equation (x^2)/4+1/10 =(x^2)/5+x/2 are x=5+sqrt(23),x=5-sqrt(23)

Find the zeros of (x^2)/4+1/10 =(x^2)/5+x/2

The zeros of (x^2)/4+1/10 =(x^2)/5+x/2 are x=5+sqrt(23),x=5-sqrt(23)

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\frac{x ^{2}}{4} + \frac{1}{10} = \frac{x ^{2}}{5} + \frac{x}{2}

x = 5 + 23, x = 5 - 23

Decimal Notation

x = 9.79583 \dots, x = 0.20416 \dots

Solution steps

\frac{x ^{2}}{4} + \frac{1}{10} = \frac{x ^{2}}{5} + \frac{x}{2}

Find Least Common Multiplier of

4, 10, 5, 2 : 20

Multiply by LCM=

20

\frac{x ^{2}}{4} \cdot 20 + \frac{1}{10} \cdot 20 = \frac{x ^{2}}{5} \cdot 20 + \frac{x}{2} \cdot 20

Simplify

5 x^{2} + 2 = 4 x^{2} + 10 x

Move

10 x

to the left side

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

Move

4 x^{2}

to the left side

x^{2} - 10 x + 2 = 0

Solve with the quadratic formula

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

(- 10)^{2} - 4 \cdot 1 \cdot 2 = 223

x_{1, 2} = \frac{- ( - 10 ) \pm 2 23}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 10 ) + 2 23}{2 \cdot 1}, x_{2} = \frac{- ( - 10 ) - 2 23}{2 \cdot 1}

x = \frac{- ( - 10 ) + 2 23}{2 \cdot 1} : 5 + 23

x = \frac{- ( - 10 ) - 2 23}{2 \cdot 1} : 5 - 23

The solutions to the quadratic equation are:

x = 5 + 23, x = 5 - 23

2 x^{2} + 15 x - 7 = 2 x

(x + 4) (x - 3) = 8

(3 x)^{2} - 4 (x + 5) (x) = 0

x, y^{3} - x y + x^{2} = 1

0.01 x^{2} - 3 x + 229 = 429 - 2 x

What are the solutions to the equation (x^2)/4+1/10 =(x^2)/5+x/2 ?
The solutions to the equation (x^2)/4+1/10 =(x^2)/5+x/2 are x=5+sqrt(23),x=5-sqrt(23)
Find the zeros of (x^2)/4+1/10 =(x^2)/5+x/2
The zeros of (x^2)/4+1/10 =(x^2)/5+x/2 are x=5+sqrt(23),x=5-sqrt(23)