What are the solutions to the equation 200x-1/4 x^2=52x+3/4 x^2+2112 ?

The solutions to the equation 200x-1/4 x^2=52x+3/4 x^2+2112 are x=132,x=16

Find the zeros of 200x-1/4 x^2=52x+3/4 x^2+2112

The zeros of 200x-1/4 x^2=52x+3/4 x^2+2112 are x=132,x=16

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200 x - \frac{1}{4} x^{2} = 52 x + \frac{3}{4} x^{2} + 2112

x = 132, x = 16

Solution steps

200 x - \frac{1}{4} x^{2} = 52 x + \frac{3}{4} x^{2} + 2112

Multiply both sides by

4

800 x - x^{2} = 208 x + 3 x^{2} + 8448

Switch sides

208 x + 3 x^{2} + 8448 = 800 x - x^{2}

Move

x^{2}

to the left side

4 x^{2} + 208 x + 8448 = 800 x

Move

800 x

to the left side

4 x^{2} - 592 x + 8448 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 592 ) \pm ( - 592 ) ^{2} - 4 \cdot 4 \cdot 8448}{2 \cdot 4}

(- 592)^{2} - 4 \cdot 4 \cdot 8448 = 464

x_{1, 2} = \frac{- ( - 592 ) \pm 464}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 592 ) + 464}{2 \cdot 4}, x_{2} = \frac{- ( - 592 ) - 464}{2 \cdot 4}

x = \frac{- ( - 592 ) + 464}{2 \cdot 4} : 132

x = \frac{- ( - 592 ) - 464}{2 \cdot 4} : 16

The solutions to the quadratic equation are:

x = 132, x = 16

3 x^{2} - 3 = 3 x

5 x^{2} + 50 x + 45 = 0

5 x^{2} = 900

5 x^{2} = 3 x^{2} + 24

5 x^{2} + 8 x = 4

What are the solutions to the equation 200x-1/4 x^2=52x+3/4 x^2+2112 ?
The solutions to the equation 200x-1/4 x^2=52x+3/4 x^2+2112 are x=132,x=16
Find the zeros of 200x-1/4 x^2=52x+3/4 x^2+2112
The zeros of 200x-1/4 x^2=52x+3/4 x^2+2112 are x=132,x=16