9(2x+1)=4(x-5)²
⇔ 18x +9 = 4.(x² -10x +25)
⇔ 18x +9 = 4x² -40x +100
⇔ -4x² +18x +40x +9 -100 = 0
⇔ -4x² +58x -91 = 0
⇔ -(4x² -58x +91) = 0
⇔ -(2x - $\frac{29}{2}$ )² + $\frac{477}{4}$ = 0
⇔ -(2x - $\frac{29}{2}$ )² = - $\frac{477}{4}$
⇔ -(2x - $\frac{29}{2}$ )² = - ( $\frac{√477}{2}$ )²
⇔ \(\left[ \begin{array}{l}2x - \frac{29}{2}=\frac{√477}{2}\\2x - \frac{29}{2}=-\frac{√477}{2}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\frac{29+3√53}{4} \\x=\frac{29-3√53}{4}\end{array} \right.\)
Vậy S= { $\frac{29 +3√53}{4}$ ; $\frac{29 -3√53}{4}$ }
