What are the solutions to the equation 4r^2-108r=-20 ?

The solutions to the equation 4r^2-108r=-20 are r=(27+sqrt(709))/2 ,r=(27-sqrt(709))/2

Find the zeros of 4r^2-108r=-20

The zeros of 4r^2-108r=-20 are r=(27+sqrt(709))/2 ,r=(27-sqrt(709))/2

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4 r^{2} - 108 r = - 20

r = \frac{27 + 709}{2}, r = \frac{27 - 709}{2}

Decimal Notation

r = 26.81352 \dots, r = 0.18647 \dots

Solution steps

4 r^{2} - 108 r = - 20

Move

20

to the left side

4 r^{2} - 108 r + 20 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 108 ) \pm ( - 108 ) ^{2} - 4 \cdot 4 \cdot 20}{2 \cdot 4}

(- 108)^{2} - 4 \cdot 4 \cdot 20 = 4709

r_{1, 2} = \frac{- ( - 108 ) \pm 4 709}{2 \cdot 4}

Separate the solutions

r_{1} = \frac{- ( - 108 ) + 4 709}{2 \cdot 4}, r_{2} = \frac{- ( - 108 ) - 4 709}{2 \cdot 4}

r = \frac{- ( - 108 ) + 4 709}{2 \cdot 4} : \frac{27 + 709}{2}

r = \frac{- ( - 108 ) - 4 709}{2 \cdot 4} : \frac{27 - 709}{2}

The solutions to the quadratic equation are:

r = \frac{27 + 709}{2}, r = \frac{27 - 709}{2}

x + (x \cdot 0.1 x) = 75

5 w + 18 \geq 8 w + 2 - 3 w

e^{x} e^{- x}

72 x - 2 x^{7}

s^{2} + 3 s + 16 = 0

What are the solutions to the equation 4r^2-108r=-20 ?
The solutions to the equation 4r^2-108r=-20 are r=(27+sqrt(709))/2 ,r=(27-sqrt(709))/2
Find the zeros of 4r^2-108r=-20
The zeros of 4r^2-108r=-20 are r=(27+sqrt(709))/2 ,r=(27-sqrt(709))/2