What are the solutions to the equation 7g-5g^2=4 ?

The solutions to the equation 7g-5g^2=4 are g= 7/10-i(sqrt(31))/(10),g= 7/10+i(sqrt(31))/(10)

Find the zeros of 7g-5g^2=4

The zeros of 7g-5g^2=4 are g= 7/10-i(sqrt(31))/(10),g= 7/10+i(sqrt(31))/(10)

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7 g - 5 g^{2} = 4

g = \frac{7}{10} - i \frac{31}{10}, g = \frac{7}{10} + i \frac{31}{10}

Solution steps

7 g - 5 g^{2} = 4

Move

4

to the left side

7 g - 5 g^{2} - 4 = 0

Write in the standard form

a x^{2} + b x + c = 0

- 5 g^{2} + 7 g - 4 = 0

Solve with the quadratic formula

g_{1, 2} = \frac{- 7 \pm 7 ^{2} - 4 ( - 5 ) ( - 4 )}{2 ( - 5 )}

Simplify

7^{2} - 4 (- 5) (- 4) : 31 i

g_{1, 2} = \frac{- 7 \pm 31 i}{2 ( - 5 )}

Separate the solutions

g_{1} = \frac{- 7 + 31 i}{2 ( - 5 )}, g_{2} = \frac{- 7 - 31 i}{2 ( - 5 )}

g = \frac{- 7 + 31 i}{2 ( - 5 )} : \frac{7}{10} - i \frac{31}{10}

g = \frac{- 7 - 31 i}{2 ( - 5 )} : \frac{7}{10} + i \frac{31}{10}

The solutions to the quadratic equation are:

g = \frac{7}{10} - i \frac{31}{10}, g = \frac{7}{10} + i \frac{31}{10}

10 r^{2} - 35 r = 0

x^{2} + 80 x + 1600 = 0

4.9 x^{2} - 205.06 x - 210 = 0

(3 x - 1)^{2} = 75

x (x - 3) = - 1

What are the solutions to the equation 7g-5g^2=4 ?
The solutions to the equation 7g-5g^2=4 are g= 7/10-i(sqrt(31))/(10),g= 7/10+i(sqrt(31))/(10)
Find the zeros of 7g-5g^2=4
The zeros of 7g-5g^2=4 are g= 7/10-i(sqrt(31))/(10),g= 7/10+i(sqrt(31))/(10)