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