What are the solutions to the equation 5x^2+13=15x ?

The solutions to the equation 5x^2+13=15x are x= 3/2+i(sqrt(35))/(10),x= 3/2-i(sqrt(35))/(10)

Find the zeros of 5x^2+13=15x

The zeros of 5x^2+13=15x are x= 3/2+i(sqrt(35))/(10),x= 3/2-i(sqrt(35))/(10)

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5 x^{2} + 13 = 15 x

x = \frac{3}{2} + i \frac{35}{10}, x = \frac{3}{2} - i \frac{35}{10}

Solution steps

5 x^{2} + 13 = 15 x

Move

15 x

to the left side

5 x^{2} + 13 - 15 x = 0

Write in the standard form

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

5 x^{2} - 15 x + 13 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 15 ) \pm ( - 15 ) ^{2} - 4 \cdot 5 \cdot 13}{2 \cdot 5}

Simplify

(- 15)^{2} - 4 \cdot 5 \cdot 13 : 35 i

x_{1, 2} = \frac{- ( - 15 ) \pm 35 i}{2 \cdot 5}

Separate the solutions

x_{1} = \frac{- ( - 15 ) + 35 i}{2 \cdot 5}, x_{2} = \frac{- ( - 15 ) - 35 i}{2 \cdot 5}

x = \frac{- ( - 15 ) + 35 i}{2 \cdot 5} : \frac{3}{2} + i \frac{35}{10}

x = \frac{- ( - 15 ) - 35 i}{2 \cdot 5} : \frac{3}{2} - i \frac{35}{10}

The solutions to the quadratic equation are:

x = \frac{3}{2} + i \frac{35}{10}, x = \frac{3}{2} - i \frac{35}{10}

x, x^{2} - k x + 100 = 0

- 3 x^{2} + 33 = 48 x

x^{2} + 10 x = 32

4 x^{2} + 5 = - 12 x

x^{2} - 5 x + 10 = 4

What are the solutions to the equation 5x^2+13=15x ?
The solutions to the equation 5x^2+13=15x are x= 3/2+i(sqrt(35))/(10),x= 3/2-i(sqrt(35))/(10)
Find the zeros of 5x^2+13=15x
The zeros of 5x^2+13=15x are x= 3/2+i(sqrt(35))/(10),x= 3/2-i(sqrt(35))/(10)