How do you solve #-5x = -3x^2# using the quadratic formula?

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Answer 1 · 2017-02-19T19:33:44

See the entire solution process below:

First, add #color(red)(3x^2)# to each side of the equation:

#color(red)(3x^2) - 5x = color(red)(3x^2) - 3x^2#

#3x^2 - 5x = 0#

Now, factor an #x# out of the expression on the left side of the equation:

#x(3x - 5) = 0#

Now, we can find the two solutions by equating each of the terms to #0# and solving:

Solution 1)

#x = 0#

Solution 2)

#3x - 5 = 0#

#3x - 5 + color(red)(5) = 0 + color(red)(5)#

#3x - 0 = 5#

#3x = 5#

#(3x)/color(red)(3) = 5/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 5/3#

#x = 5/3#

The solution is: #x = 0# and #x = 5/3#