How do you use the quadratic formula to solve #3/4(x-1)^2=-4/3x+4/5#?

1 Answer
Jun 20, 2017

Answer:

Before one uses the quadratic formula, one must write the equation in the form:

#ax^2+bx+c=0#

Then substitute, a, b, and c into the formula:

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

Explanation:

Given: #3/4(x-1)^2=-4/3x+4/5#

Multiply both sides of the equation by the factors: #(3)(4)(5)#

#45(x-1)^2=-80x+48#

Expand the square:

#45(x^2-2x+1) = -80x +48#

Distribute the 45:

#45x^2-90x+45 = -80x +48#

Combine like terms:

#45x^2-10x-3 = 0#

By observation, #a =45, b = -10, and c = -3#

Substitute into the formula:

#x = (10+-sqrt((-10)^2-4(45)(-3)))/(2(45))#

#x = (10+-sqrt(640))/90#

#x = (10+-8sqrt(10))/90#

#x = (10-8sqrt10)/90# and #x = (10+8sqrt10)/90#