What are the solutions to the equation 2(w-2)(w+1)-(w+3)=0 ?

The solutions to the equation 2(w-2)(w+1)-(w+3)=0 are w=(3+sqrt(65))/4 ,w=(3-sqrt(65))/4

Find the zeros of 2(w-2)(w+1)-(w+3)=0

The zeros of 2(w-2)(w+1)-(w+3)=0 are w=(3+sqrt(65))/4 ,w=(3-sqrt(65))/4

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2 (w - 2) (w + 1) - (w + 3) = 0

w = \frac{3 + 65}{4}, w = \frac{3 - 65}{4}

Decimal Notation

w = 2.76556 \dots, w = - 1.26556 \dots

Solution steps

2 (w - 2) (w + 1) - (w + 3) = 0

Expand

2 (w - 2) (w + 1) - (w + 3) : 2 w^{2} - 3 w - 7

2 w^{2} - 3 w - 7 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 2 ( - 7 )}{2 \cdot 2}

(- 3)^{2} - 4 \cdot 2 (- 7) = 65

w_{1, 2} = \frac{- ( - 3 ) \pm 65}{2 \cdot 2}

Separate the solutions

w_{1} = \frac{- ( - 3 ) + 65}{2 \cdot 2}, w_{2} = \frac{- ( - 3 ) - 65}{2 \cdot 2}

w = \frac{- ( - 3 ) + 65}{2 \cdot 2} : \frac{3 + 65}{4}

w = \frac{- ( - 3 ) - 65}{2 \cdot 2} : \frac{3 - 65}{4}

The solutions to the quadratic equation are:

w = \frac{3 + 65}{4}, w = \frac{3 - 65}{4}

5000 x^{2} + 5000 x - 9254.27 = 0

6 x^{2} + x - 12 = 0

1.5 t - 0.12 t^{2} = 0

x^{2} - 2 x - \frac{3}{2} = 0

6 x^{2} - 25 x + 25 = 0

What are the solutions to the equation 2(w-2)(w+1)-(w+3)=0 ?
The solutions to the equation 2(w-2)(w+1)-(w+3)=0 are w=(3+sqrt(65))/4 ,w=(3-sqrt(65))/4
Find the zeros of 2(w-2)(w+1)-(w+3)=0
The zeros of 2(w-2)(w+1)-(w+3)=0 are w=(3+sqrt(65))/4 ,w=(3-sqrt(65))/4