What are the solutions to the equation 124=0.006a^2-0.02a+120 ?

The solutions to the equation 124=0.006a^2-0.02a+120 are a=(5(1+sqrt(241)))/3 ,a=(5(1-sqrt(241)))/3

Find the zeros of 124=0.006a^2-0.02a+120

The zeros of 124=0.006a^2-0.02a+120 are a=(5(1+sqrt(241)))/3 ,a=(5(1-sqrt(241)))/3

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124 = 0.006 a^{2} - 0.02 a + 120

a = \frac{5 ( 1 + 241 )}{3}, a = \frac{5 ( 1 - 241 )}{3}

Decimal Notation

a = 27.54029 \dots, a = - 24.20695 \dots

Solution steps

124 = 0.006 a^{2} - 0.02 a + 120

Multiply both sides by

1000

124000 = 6 a^{2} - 20 a + 120000

Switch sides

6 a^{2} - 20 a + 120000 = 124000

Move

124000

to the left side

6 a^{2} - 20 a - 4000 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 6 ( - 4000 )}{2 \cdot 6}

(- 20)^{2} - 4 \cdot 6 (- 4000) = 20241

a_{1, 2} = \frac{- ( - 20 ) \pm 20 241}{2 \cdot 6}

Separate the solutions

a_{1} = \frac{- ( - 20 ) + 20 241}{2 \cdot 6}, a_{2} = \frac{- ( - 20 ) - 20 241}{2 \cdot 6}

a = \frac{- ( - 20 ) + 20 241}{2 \cdot 6} : \frac{5 ( 1 + 241 )}{3}

a = \frac{- ( - 20 ) - 20 241}{2 \cdot 6} : \frac{5 ( 1 - 241 )}{3}

The solutions to the quadratic equation are:

a = \frac{5 ( 1 + 241 )}{3}, a = \frac{5 ( 1 - 241 )}{3}

- x^{2} - 2 x + 7 = - 17

\frac{1}{4} x^{2} - x - 1 = \frac{1}{16} x^{2} - \frac{1}{4} x + \frac{5}{4}

X, 4 X^{2} + 9 y^{2} = 36

t^{2} + 2 t - 5 = 0

x^{2} + 1 = 26

What are the solutions to the equation 124=0.006a^2-0.02a+120 ?
The solutions to the equation 124=0.006a^2-0.02a+120 are a=(5(1+sqrt(241)))/3 ,a=(5(1-sqrt(241)))/3
Find the zeros of 124=0.006a^2-0.02a+120
The zeros of 124=0.006a^2-0.02a+120 are a=(5(1+sqrt(241)))/3 ,a=(5(1-sqrt(241)))/3