What are the solutions to the equation 12r^2-8r-27=-5 ?

The solutions to the equation 12r^2-8r-27=-5 are r=(2+sqrt(70))/6 ,r=(2-sqrt(70))/6

Find the zeros of 12r^2-8r-27=-5

The zeros of 12r^2-8r-27=-5 are r=(2+sqrt(70))/6 ,r=(2-sqrt(70))/6

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12 r^{2} - 8 r - 27 = - 5

r = \frac{2 + 70}{6}, r = \frac{2 - 70}{6}

Decimal Notation

r = 1.72776 \dots, r = - 1.06110 \dots

Solution steps

12 r^{2} - 8 r - 27 = - 5

Move

5

to the left side

12 r^{2} - 8 r - 22 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 12 ( - 22 )}{2 \cdot 12}

(- 8)^{2} - 4 \cdot 12 (- 22) = 470

r_{1, 2} = \frac{- ( - 8 ) \pm 4 70}{2 \cdot 12}

Separate the solutions

r_{1} = \frac{- ( - 8 ) + 4 70}{2 \cdot 12}, r_{2} = \frac{- ( - 8 ) - 4 70}{2 \cdot 12}

r = \frac{- ( - 8 ) + 4 70}{2 \cdot 12} : \frac{2 + 70}{6}

r = \frac{- ( - 8 ) - 4 70}{2 \cdot 12} : \frac{2 - 70}{6}

The solutions to the quadratic equation are:

r = \frac{2 + 70}{6}, r = \frac{2 - 70}{6}

u^{2} - 10 u = - 26

x^{2} = - 2 x + 2

x^{2} - 20 x - 96 = 0

2 x^{2} - 28 x + 80 = 0

r^{2} + r + \frac{1}{4} = 0

What are the solutions to the equation 12r^2-8r-27=-5 ?
The solutions to the equation 12r^2-8r-27=-5 are r=(2+sqrt(70))/6 ,r=(2-sqrt(70))/6
Find the zeros of 12r^2-8r-27=-5
The zeros of 12r^2-8r-27=-5 are r=(2+sqrt(70))/6 ,r=(2-sqrt(70))/6