What are the solutions to the equation 4x^2=31x+8 ?

The solutions to the equation 4x^2=31x+8 are x=8,x=-1/4

Find the zeros of 4x^2=31x+8

The zeros of 4x^2=31x+8 are x=8,x=-1/4

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4 x^{2} = 31 x + 8

x = 8, x = - \frac{1}{4}

Decimal Notation

x = 8, x = - 0.25

Solution steps

4 x^{2} = 31 x + 8

Move

8

to the left side

4 x^{2} - 8 = 31 x

Move

31 x

to the left side

4 x^{2} - 8 - 31 x = 0

Write in the standard form

a x^{2} + b x + c = 0

4 x^{2} - 31 x - 8 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 31 ) \pm ( - 31 ) ^{2} - 4 \cdot 4 ( - 8 )}{2 \cdot 4}

(- 31)^{2} - 4 \cdot 4 (- 8) = 33

x_{1, 2} = \frac{- ( - 31 ) \pm 33}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 31 ) + 33}{2 \cdot 4}, x_{2} = \frac{- ( - 31 ) - 33}{2 \cdot 4}

x = \frac{- ( - 31 ) + 33}{2 \cdot 4} : 8

x = \frac{- ( - 31 ) - 33}{2 \cdot 4} : - \frac{1}{4}

The solutions to the quadratic equation are:

x = 8, x = - \frac{1}{4}

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

x, 2 = 3 x^{2} - 4 y^{3}

x^{2} - 10 x = 5

x, f^{2} (x) = 2 x^{2} - 1

y, x^{2} + y^{2} - 3 x y + 4 = 0

What are the solutions to the equation 4x^2=31x+8 ?
The solutions to the equation 4x^2=31x+8 are x=8,x=-1/4
Find the zeros of 4x^2=31x+8
The zeros of 4x^2=31x+8 are x=8,x=-1/4