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

Hello from MrBillDoesMath!

   (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

7200

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all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: