What are the solutions to the equation 5r^2-7r+8=r^2+16r+14 ?

The solutions to the equation 5r^2-7r+8=r^2+16r+14 are r=6,r=-1/4

Find the zeros of 5r^2-7r+8=r^2+16r+14

The zeros of 5r^2-7r+8=r^2+16r+14 are r=6,r=-1/4

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5 r^{2} - 7 r + 8 = r^{2} + 16 r + 14

r = 6, r = - \frac{1}{4}

Decimal Notation

r = 6, r = - 0.25

Solution steps

5 r^{2} - 7 r + 8 = r^{2} + 16 r + 14

Move

14

to the left side

5 r^{2} - 7 r - 6 = r^{2} + 16 r

Move

16 r

to the left side

5 r^{2} - 23 r - 6 = r^{2}

Move

r^{2}

to the left side

4 r^{2} - 23 r - 6 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 23 ) \pm ( - 23 ) ^{2} - 4 \cdot 4 ( - 6 )}{2 \cdot 4}

(- 23)^{2} - 4 \cdot 4 (- 6) = 25

r_{1, 2} = \frac{- ( - 23 ) \pm 25}{2 \cdot 4}

Separate the solutions

r_{1} = \frac{- ( - 23 ) + 25}{2 \cdot 4}, r_{2} = \frac{- ( - 23 ) - 25}{2 \cdot 4}

r = \frac{- ( - 23 ) + 25}{2 \cdot 4} : 6

r = \frac{- ( - 23 ) - 25}{2 \cdot 4} : - \frac{1}{4}

The solutions to the quadratic equation are:

r = 6, r = - \frac{1}{4}

4 x^{2} + 4 x - 2 = 7 x

6 x (1 - x) = x

- 16 x^{2} + 240 x + 180 = 0

9 x^{2} - 30 x - 25 = 0

9 x^{2} - 8 x = 0

What are the solutions to the equation 5r^2-7r+8=r^2+16r+14 ?
The solutions to the equation 5r^2-7r+8=r^2+16r+14 are r=6,r=-1/4
Find the zeros of 5r^2-7r+8=r^2+16r+14
The zeros of 5r^2-7r+8=r^2+16r+14 are r=6,r=-1/4