What are the solutions to the equation 4/9 a^2-1/4 a=5 ?

The solutions to the equation 4/9 a^2-1/4 a=5 are a=(9+3sqrt(1289))/(32),a=(9-3sqrt(1289))/(32)

Find the zeros of 4/9 a^2-1/4 a=5

The zeros of 4/9 a^2-1/4 a=5 are a=(9+3sqrt(1289))/(32),a=(9-3sqrt(1289))/(32)

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\frac{4}{9} a^{2} - \frac{1}{4} a = 5

a = \frac{9 + 3 1289}{32}, a = \frac{9 - 3 1289}{32}

Decimal Notation

a = 3.64712 \dots, a = - 3.08462 \dots

Solution steps

\frac{4}{9} a^{2} - \frac{1}{4} a = 5

Find Least Common Multiplier of

9, 4 : 36

Multiply by LCM=

36

\frac{4}{9} a^{2} \cdot 36 - \frac{1}{4} a \cdot 36 = 5 \cdot 36

Simplify

16 a^{2} - 9 a = 180

Move

180

to the left side

16 a^{2} - 9 a - 180 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 16 ( - 180 )}{2 \cdot 16}

(- 9)^{2} - 4 \cdot 16 (- 180) = 31289

a_{1, 2} = \frac{- ( - 9 ) \pm 3 1289}{2 \cdot 16}

Separate the solutions

a_{1} = \frac{- ( - 9 ) + 3 1289}{2 \cdot 16}, a_{2} = \frac{- ( - 9 ) - 3 1289}{2 \cdot 16}

a = \frac{- ( - 9 ) + 3 1289}{2 \cdot 16} : \frac{9 + 3 1289}{32}

a = \frac{- ( - 9 ) - 3 1289}{2 \cdot 16} : \frac{9 - 3 1289}{32}

The solutions to the quadratic equation are:

a = \frac{9 + 3 1289}{32}, a = \frac{9 - 3 1289}{32}

(5 + y)^{2} + y^{2} = 37

x^{2} + 6 x = - 5

x, f = 2 x^{2} - 2 y

- 16 t^{2} + 1600 = 0

8 (3 x^{2} + 4) = 0

What are the solutions to the equation 4/9 a^2-1/4 a=5 ?
The solutions to the equation 4/9 a^2-1/4 a=5 are a=(9+3sqrt(1289))/(32),a=(9-3sqrt(1289))/(32)
Find the zeros of 4/9 a^2-1/4 a=5
The zeros of 4/9 a^2-1/4 a=5 are a=(9+3sqrt(1289))/(32),a=(9-3sqrt(1289))/(32)