Find all real or imaginary solutions to the equation 4x2 8x

Find all real or imaginary solutions to the equation.

4x^2 -8x = +7


Please help and explain . I forgot how to do this. I see why it yields an imaginary but I don\'t know how to solve for imaginaries.

Solution

4x^2 -8x = +7

4x^2 -8x -7 =0

Use quadratic root formula to solve the equation:

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

x = (8 +/-sqrt(64 + 112) )/8

= (8 +/- 4sqrt11)/8

= 1 +/ 1.658

I dont see a imgainary root if the given equation is :4x^2 -8x = +7

If the equation is 4x^2 -8x +7 =0

Then ,x = (8 +/- sqrt(4 -112) )8

we have imaginary roots as b^2 -4ac <0

= (8 +/- sqr(-108))/8

= 1+/- i*sqrt(108)/8

= 1+/- i6*sqrt3/8

=1 +/- i*1.299

= 1 +/-1.3i

So, root are x = 1+1.3*i , 1- 1.3*i