You can put this solution on YOUR website! . Find all real values of x that satisfy the equation [(3x+4)/(5x+1)]^2+(3x+4)/(5x+1)=12
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+ = 12.
Introduce new variable u = . Then your equation becomes this quadratic equation
= 0.
Factor left side polynomial. You will get
(u+4)*(u-3) = 0,
which has two roots u= -4 and u= 3.
a) Case u= -4: then = -4 ====> 3x+4 = (-4)*(5x+1) ====> 3x+4 = -20x-4 ====> 23x = -8 ====> x = .
b) Case u= 3: then = 3 ====> 3x+4 = 3*(5x+1) ====> 3x+4 = 15x+3 ====> 12x = 1 ====> x = .
Answer. The original equation has two solutions x= and x= .
Introducing new variable is a standard method of solution non-linear equations like this one.
