What are the solutions to the equation 3r^2-12r-77=5 ?

The solutions to the equation 3r^2-12r-77=5 are r=(6+sqrt(282))/3 ,r=(6-sqrt(282))/3

Find the zeros of 3r^2-12r-77=5

The zeros of 3r^2-12r-77=5 are r=(6+sqrt(282))/3 ,r=(6-sqrt(282))/3

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3 r^{2} - 12 r - 77 = 5

r = \frac{6 + 282}{3}, r = \frac{6 - 282}{3}

Decimal Notation

r = 7.59761 \dots, r = - 3.59761 \dots

Solution steps

3 r^{2} - 12 r - 77 = 5

Move

5

to the left side

3 r^{2} - 12 r - 82 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 ( - 82 )}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 (- 82) = 2282

r_{1, 2} = \frac{- ( - 12 ) \pm 2 282}{2 \cdot 3}

Separate the solutions

r_{1} = \frac{- ( - 12 ) + 2 282}{2 \cdot 3}, r_{2} = \frac{- ( - 12 ) - 2 282}{2 \cdot 3}

r = \frac{- ( - 12 ) + 2 282}{2 \cdot 3} : \frac{6 + 282}{3}

r = \frac{- ( - 12 ) - 2 282}{2 \cdot 3} : \frac{6 - 282}{3}

The solutions to the quadratic equation are:

r = \frac{6 + 282}{3}, r = \frac{6 - 282}{3}

4 x^{2} - 8 x = 5

8 k^{2} + 16 k - 26 = - 2

6 x^{2} + 12 x = 48

- 12 y = 4 y^{2} + 9

x^{2} + 8 x + 16 = - 4

What are the solutions to the equation 3r^2-12r-77=5 ?
The solutions to the equation 3r^2-12r-77=5 are r=(6+sqrt(282))/3 ,r=(6-sqrt(282))/3
Find the zeros of 3r^2-12r-77=5
The zeros of 3r^2-12r-77=5 are r=(6+sqrt(282))/3 ,r=(6-sqrt(282))/3