How do you solve #3x^2 - 4x = 2# using the quadratic formula?

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Answer 1 · 2016-05-27T13:43:10

#1.721# and #-.387#

First you want to get all of the variable on the same side

#3x^2 - 4x = 2#

#3x^2 - 4x - 2 = 0#

Remember that #ax^2 + bx + c = 0# so #a = 3#, #b = -4#, and #c = -2#

#x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)#

so

#x_(1,2) = ( -(-4) +- sqrt( (-4)^2 - 4(3)(-2)))/(2(3))#

#x_(1,2) = ( 4 +- sqrt( 16 + 24 ) ) / 6#

#x_(1,2) = ( 4 +- sqrt( 40 ) ) / 6#

Since #sqrt 40 = 6.325# (rounded), sub that in and add/subtract according to the equation

#(4 + 6.325) / 6 = 1.721#

#(4 - 6.325) / 6 = - .387#