How do you solve #3x^2-8=0# using the quadratic formula?

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Answer 1 · 2017-07-17T21:34:08

See a solution process below:

We can rewrite this equation as:

#3x^2 + 0x - 8 = 0#

For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by:

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

Substituting #3# for #a#; #0# for #b# and #-8# for #c# gives:

#x = (-0 +- sqrt(0^2 - (4 * 3 * -8)))/(2 * 3)#

#x = +- sqrt(0 - (-96))/(6)#

#x = +- sqrt(+96)/(6)#

#x = +- sqrt(16 * 6)/(6)#

#x = +- (sqrt(16) * sqrt(6))/(6)#

#x = +- (4 * sqrt(6))/6#

#x = +- (2 * 2 * sqrt(6))/(2 * 3)#

#x = +- (color(red)(cancel(color(black)(2))) * 2 * sqrt(6))/(color(red)(cancel(color(black)(2))) * 3)#

#x = +- (2sqrt(6))/3#