What are the solutions to the equation 7x^2-2x+3=5x^2-10 ?

The solutions to the equation 7x^2-2x+3=5x^2-10 are x= 1/2+i 5/2 ,x= 1/2-i 5/2

Find the zeros of 7x^2-2x+3=5x^2-10

The zeros of 7x^2-2x+3=5x^2-10 are x= 1/2+i 5/2 ,x= 1/2-i 5/2

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7 x^{2} - 2 x + 3 = 5 x^{2} - 10

x = \frac{1}{2} + i \frac{5}{2}, x = \frac{1}{2} - i \frac{5}{2}

Solution steps

7 x^{2} - 2 x + 3 = 5 x^{2} - 10

Move

10

to the left side

7 x^{2} - 2 x + 13 = 5 x^{2}

Move

5 x^{2}

to the left side

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

Solve with the quadratic formula

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

Simplify

(- 2)^{2} - 4 \cdot 2 \cdot 13 : 10 i

x_{1, 2} = \frac{- ( - 2 ) \pm 10 i}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 10 i}{2 \cdot 2}, x_{2} = \frac{- ( - 2 ) - 10 i}{2 \cdot 2}

x = \frac{- ( - 2 ) + 10 i}{2 \cdot 2} : \frac{1}{2} + i \frac{5}{2}

x = \frac{- ( - 2 ) - 10 i}{2 \cdot 2} : \frac{1}{2} - i \frac{5}{2}

The solutions to the quadratic equation are:

x = \frac{1}{2} + i \frac{5}{2}, x = \frac{1}{2} - i \frac{5}{2}

7 x (x - 8) = 0

- 3 x^{2} - 6 x + 24 = 0

x^{2} - 7 x + 9 = 4

20 a^{2} + 13 a + 2 = 0

(x - 3) (x + 4) + 8 = x

What are the solutions to the equation 7x^2-2x+3=5x^2-10 ?
The solutions to the equation 7x^2-2x+3=5x^2-10 are x= 1/2+i 5/2 ,x= 1/2-i 5/2
Find the zeros of 7x^2-2x+3=5x^2-10
The zeros of 7x^2-2x+3=5x^2-10 are x= 1/2+i 5/2 ,x= 1/2-i 5/2