What are the solutions to the equation 7/4 x^2+4x+5=0 ?

The solutions to the equation 7/4 x^2+4x+5=0 are x=-8/7+i(2sqrt(19))/7 ,x=-8/7-i(2sqrt(19))/7

Find the zeros of 7/4 x^2+4x+5=0

The zeros of 7/4 x^2+4x+5=0 are x=-8/7+i(2sqrt(19))/7 ,x=-8/7-i(2sqrt(19))/7

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\frac{7}{4} x^{2} + 4 x + 5 = 0

x = - \frac{8}{7} + i \frac{2 19}{7}, x = - \frac{8}{7} - i \frac{2 19}{7}

Solution steps

\frac{7}{4} x^{2} + 4 x + 5 = 0

Multiply both sides by

4

7 x^{2} + 16 x + 20 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 7 \cdot 20}{2 \cdot 7}

Simplify

1 6^{2} - 4 \cdot 7 \cdot 20 : 419 i

x_{1, 2} = \frac{- 16 \pm 4 19 i}{2 \cdot 7}

Separate the solutions

x_{1} = \frac{- 16 + 4 19 i}{2 \cdot 7}, x_{2} = \frac{- 16 - 4 19 i}{2 \cdot 7}

x = \frac{- 16 + 4 19 i}{2 \cdot 7} : - \frac{8}{7} + i \frac{2 19}{7}

x = \frac{- 16 - 4 19 i}{2 \cdot 7} : - \frac{8}{7} - i \frac{2 19}{7}

The solutions to the quadratic equation are:

x = - \frac{8}{7} + i \frac{2 19}{7}, x = - \frac{8}{7} - i \frac{2 19}{7}

3 (3 x - 2) = (x - 4) (4 - x)

3 (3 x - 1)^{2} + 34 = 46

3 x^{2} + 1 = - 25 x - 7

x, a^{2} x^{2} + (a y - a) x = 2 + 2 y

5 x^{2} - 10 x + 8 = 0

What are the solutions to the equation 7/4 x^2+4x+5=0 ?
The solutions to the equation 7/4 x^2+4x+5=0 are x=-8/7+i(2sqrt(19))/7 ,x=-8/7-i(2sqrt(19))/7
Find the zeros of 7/4 x^2+4x+5=0
The zeros of 7/4 x^2+4x+5=0 are x=-8/7+i(2sqrt(19))/7 ,x=-8/7-i(2sqrt(19))/7