What are the solutions to the equation 5x^2-3x+a-1=0 ?

The solutions to the equation 5x^2-3x+a-1=0 are x=(3+sqrt(-20a+29))/(10),x=(3-sqrt(-20a+29))/(10)

Find the zeros of 5x^2-3x+a-1=0

The zeros of 5x^2-3x+a-1=0 are x=(3+sqrt(-20a+29))/(10),x=(3-sqrt(-20a+29))/(10)

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5 x^{2} - 3 x + a - 1 = 0

x = \frac{3 + - 20 a + 29}{10}, x = \frac{3 - - 20 a + 29}{10}

Solution steps

5 x^{2} - 3 x + a - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 5 ( a - 1 )}{2 \cdot 5}

Simplify

(- 3)^{2} - 4 \cdot 5 (a - 1) : - 20 a + 29

x_{1, 2} = \frac{- ( - 3 ) \pm - 20 a + 29}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + - 20 a + 29}{2 \cdot 5}, x_{2} = \frac{- ( - 3 ) - - 20 a + 29}{2 \cdot 5}

x = \frac{- ( - 3 ) + - 20 a + 29}{2 \cdot 5} : \frac{3 + - 20 a + 29}{10}

x = \frac{- ( - 3 ) - - 20 a + 29}{2 \cdot 5} : \frac{3 - - 20 a + 29}{10}

The solutions to the quadratic equation are:

x = \frac{3 + - 20 a + 29}{10}, x = \frac{3 - - 20 a + 29}{10}

3 x^{2} + 29 x - 10 = 0

0 = - x^{2} - 27

x^{2} - 8 = - 36

(x^{2} - 2) 2 - 10 (x^{2} - 2) + 21 = 0

10 x^{2} + 5 x = 0

What are the solutions to the equation 5x^2-3x+a-1=0 ?
The solutions to the equation 5x^2-3x+a-1=0 are x=(3+sqrt(-20a+29))/(10),x=(3-sqrt(-20a+29))/(10)
Find the zeros of 5x^2-3x+a-1=0
The zeros of 5x^2-3x+a-1=0 are x=(3+sqrt(-20a+29))/(10),x=(3-sqrt(-20a+29))/(10)