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Find the roots of the equation below 7x^2+3=8x

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Hello from MrBillDoesMath!

Answer: (1/7) * ( 4 +\- sqrt(5) i)

where i = sqrt(-1)

Discussion:

The solutions of the quadratic equation ax^2 + bx + c = 0 are given by

x = ( -b +\- sqrt(b^2 - 4ac) )/2a.

The equation 7 x^2 + 3 = 8x can be rewritten as

7x^2 - 8x + 3 = 0.

Using a = 7, b = -8 and c = 3 in the quadratic formula gives:

x = (8 +\- sqrt ( (-8)^2 - 4*7*3) ) / (2*7)

= ( 8 +\- sqrt( 64 - 84)) /(2*7)

= ( 8 +\- sqrt( -20) ) / (2*7)

= ( 8 +\- sqrt( -20) ) / 14

= 8/14 +\- sqrt(5 *4 * -1) /14

= 4/7 +\- 2 sqrt(5) *i /14

As 2/14 = 1/7 in the second term

= 4/7 +\- sqrt(5) *i /7

Factor 1/7 from each term.

= (1/7) * ( 4 +\- sqrt(5) i)


Thank you,

MrB


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