Question

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

Answer 1

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