What are the solutions to the equation 4r^2-r=5 ?

The solutions to the equation 4r^2-r=5 are r= 5/4 ,r=-1

Find the zeros of 4r^2-r=5

The zeros of 4r^2-r=5 are r= 5/4 ,r=-1

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4 r^{2} - r = 5

r = \frac{5}{4}, r = - 1

Decimal Notation

r = 1.25, r = - 1

Solution steps

4 r^{2} - r = 5

Move

5

to the left side

4 r^{2} - r - 5 = 0

Solve with the quadratic formula

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

(- 1)^{2} - 4 \cdot 4 (- 5) = 9

r_{1, 2} = \frac{- ( - 1 ) \pm 9}{2 \cdot 4}

Separate the solutions

r_{1} = \frac{- ( - 1 ) + 9}{2 \cdot 4}, r_{2} = \frac{- ( - 1 ) - 9}{2 \cdot 4}

r = \frac{- ( - 1 ) + 9}{2 \cdot 4} : \frac{5}{4}

r = \frac{- ( - 1 ) - 9}{2 \cdot 4} : - 1

The solutions to the quadratic equation are:

r = \frac{5}{4}, r = - 1

5 x^{2} + 12 x - 4 = 0

- 4 x^{2} - 48 x - 208 = 0

x^{2} + 10 = 6 x

x^{2} + 10 = 25

x, x^{2} + (\frac{4 x}{3})^{2} = 225

What are the solutions to the equation 4r^2-r=5 ?
The solutions to the equation 4r^2-r=5 are r= 5/4 ,r=-1
Find the zeros of 4r^2-r=5
The zeros of 4r^2-r=5 are r= 5/4 ,r=-1