What are the solutions to the equation 4x^2=13x-75 ?

The solutions to the equation 4x^2=13x-75 are x= 13/8+i(sqrt(1031))/8 ,x= 13/8-i(sqrt(1031))/8

Find the zeros of 4x^2=13x-75

The zeros of 4x^2=13x-75 are x= 13/8+i(sqrt(1031))/8 ,x= 13/8-i(sqrt(1031))/8

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4 x^{2} = 13 x - 75

x = \frac{13}{8} + i \frac{1031}{8}, x = \frac{13}{8} - i \frac{1031}{8}

Solution steps

4 x^{2} = 13 x - 75

Move

75

to the left side

4 x^{2} + 75 = 13 x

Move

13 x

to the left side

4 x^{2} + 75 - 13 x = 0

Write in the standard form

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

4 x^{2} - 13 x + 75 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 \cdot 4 \cdot 75}{2 \cdot 4}

Simplify

(- 13)^{2} - 4 \cdot 4 \cdot 75 : 1031 i

x_{1, 2} = \frac{- ( - 13 ) \pm 1031 i}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 13 ) + 1031 i}{2 \cdot 4}, x_{2} = \frac{- ( - 13 ) - 1031 i}{2 \cdot 4}

x = \frac{- ( - 13 ) + 1031 i}{2 \cdot 4} : \frac{13}{8} + i \frac{1031}{8}

x = \frac{- ( - 13 ) - 1031 i}{2 \cdot 4} : \frac{13}{8} - i \frac{1031}{8}

The solutions to the quadratic equation are:

x = \frac{13}{8} + i \frac{1031}{8}, x = \frac{13}{8} - i \frac{1031}{8}

x^{2} + 10 x + 25 = 7

6 4^{\frac{2}{3}} 6 4^{\frac{2}{3}}

n^{2} - n - 20

14 x^{2} - 28 = 0

- 5 m^{2} - 15 m + 50

What are the solutions to the equation 4x^2=13x-75 ?
The solutions to the equation 4x^2=13x-75 are x= 13/8+i(sqrt(1031))/8 ,x= 13/8-i(sqrt(1031))/8
Find the zeros of 4x^2=13x-75
The zeros of 4x^2=13x-75 are x= 13/8+i(sqrt(1031))/8 ,x= 13/8-i(sqrt(1031))/8