What are the solutions to the equation 1/4 y^2-3/5 y-1/4 =0 ?

The solutions to the equation 1/4 y^2-3/5 y-1/4 =0 are y=(6+sqrt(61))/5 ,y=(6-sqrt(61))/5

Find the zeros of 1/4 y^2-3/5 y-1/4 =0

The zeros of 1/4 y^2-3/5 y-1/4 =0 are y=(6+sqrt(61))/5 ,y=(6-sqrt(61))/5

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\frac{1}{4} y^{2} - \frac{3}{5} y - \frac{1}{4} = 0

y = \frac{6 + 61}{5}, y = \frac{6 - 61}{5}

Decimal Notation

y = 2.76204 \dots, y = - 0.36204 \dots

Solution steps

\frac{1}{4} y^{2} - \frac{3}{5} y - \frac{1}{4} = 0

Find Least Common Multiplier of

4, 5 : 20

Multiply by LCM=

20

\frac{1}{4} y^{2} \cdot 20 - \frac{3}{5} y \cdot 20 - \frac{1}{4} \cdot 20 = 0 \cdot 20

Simplify

5 y^{2} - 12 y - 5 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 5 ( - 5 )}{2 \cdot 5}

(- 12)^{2} - 4 \cdot 5 (- 5) = 261

y_{1, 2} = \frac{- ( - 12 ) \pm 2 61}{2 \cdot 5}

Separate the solutions

y_{1} = \frac{- ( - 12 ) + 2 61}{2 \cdot 5}, y_{2} = \frac{- ( - 12 ) - 2 61}{2 \cdot 5}

y = \frac{- ( - 12 ) + 2 61}{2 \cdot 5} : \frac{6 + 61}{5}

y = \frac{- ( - 12 ) - 2 61}{2 \cdot 5} : \frac{6 - 61}{5}

The solutions to the quadratic equation are:

y = \frac{6 + 61}{5}, y = \frac{6 - 61}{5}

x (x + 3) = 8 x - 2

0 = 16 - x^{2}

12 x^{2} + 8 x - 1 = 0

x^{2} + 3 x - 35 = 3 x + 13 x + 1

15 + 0.005 V^{1} = 10 + 0.02 V^{2}

What are the solutions to the equation 1/4 y^2-3/5 y-1/4 =0 ?
The solutions to the equation 1/4 y^2-3/5 y-1/4 =0 are y=(6+sqrt(61))/5 ,y=(6-sqrt(61))/5
Find the zeros of 1/4 y^2-3/5 y-1/4 =0
The zeros of 1/4 y^2-3/5 y-1/4 =0 are y=(6+sqrt(61))/5 ,y=(6-sqrt(61))/5