Answer
{$\frac{-3 \pm \sqrt (41)}{8}$}
Work Step by Step
Step 1: $(4x-1)(x+2)=4x$
Step 2: $4x(x+2)-1(x+2)=4x$
Step 3: $4x^{2}+8x-x-2=4x$
Step 4: $4x^{2}+7x-2=4x$
Step 5: Subtracting $4x$ from both sides of the equation, $4x^{2}+7x-2-4x=4x-4x$
Step 6: $4x^{2}+3x-2=0$
Step 7: Comparing $4x^{2}+3x-2=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=4$, $b=3$ and $c=-2$
Step 8: The quadratic formula is:
$x=\frac{-b \pm \sqrt (b^{2}-4ac)}{2a}$
Step 9: Substituting the values of a,b and c in the formula:
$x=\frac{-(3) \pm \sqrt ((3)^{2}-4(4)(-2))}{2(4)}$
Step 10: $x=\frac{-3 \pm \sqrt (9+32)}{8}$
Step 11: $x=\frac{-3 \pm \sqrt (41)}{8}$
Step 12: Therefore, the solution set is {$\frac{-3 \pm \sqrt (41)}{8}$}.
