What are the solutions to the equation 10q^2-20q+20=60-15q ?

The solutions to the equation 10q^2-20q+20=60-15q are q=(1+sqrt(65))/4 ,q=(1-sqrt(65))/4

Find the zeros of 10q^2-20q+20=60-15q

The zeros of 10q^2-20q+20=60-15q are q=(1+sqrt(65))/4 ,q=(1-sqrt(65))/4

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10 q^{2} - 20 q + 20 = 60 - 15 q

q = \frac{1 + 65}{4}, q = \frac{1 - 65}{4}

Decimal Notation

q = 2.26556 \dots, q = - 1.76556 \dots

Solution steps

10 q^{2} - 20 q + 20 = 60 - 15 q

Move

15 q

to the left side

10 q^{2} - 5 q + 20 = 60

Move

60

to the left side

10 q^{2} - 5 q - 40 = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 10 ( - 40 )}{2 \cdot 10}

(- 5)^{2} - 4 \cdot 10 (- 40) = 565

q_{1, 2} = \frac{- ( - 5 ) \pm 5 65}{2 \cdot 10}

Separate the solutions

q_{1} = \frac{- ( - 5 ) + 5 65}{2 \cdot 10}, q_{2} = \frac{- ( - 5 ) - 5 65}{2 \cdot 10}

q = \frac{- ( - 5 ) + 5 65}{2 \cdot 10} : \frac{1 + 65}{4}

q = \frac{- ( - 5 ) - 5 65}{2 \cdot 10} : \frac{1 - 65}{4}

The solutions to the quadratic equation are:

q = \frac{1 + 65}{4}, q = \frac{1 - 65}{4}

3 y^{2} - 72 = 0

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

\frac{x ^{2}}{9} = 1

s^{2} + s + 2

5 x^{2} = 2 x + 3

What are the solutions to the equation 10q^2-20q+20=60-15q ?
The solutions to the equation 10q^2-20q+20=60-15q are q=(1+sqrt(65))/4 ,q=(1-sqrt(65))/4
Find the zeros of 10q^2-20q+20=60-15q
The zeros of 10q^2-20q+20=60-15q are q=(1+sqrt(65))/4 ,q=(1-sqrt(65))/4