Question

$x(x - 1) = 11x + 21$

Answer 1

x(x - 1) = 11x + 21
x² - x = 11x + 21
x² - x - 11x - 21 = 0
x² - 12x - 21 = 0

a = 1; b = -12; c = -21

$\displaystyle \mathsf{\Delta = b^2 - 4.a.c}\\ \displaystyle \mathsf{\Delta = (-12)^2 - 4.(1).((-21)}\\ \displaystyle \mathsf{\Delta = 144 + 84}\\ \displaystyle \mathsf{\Delta = 228 }$

$\displaystyle \mathsf{x = \frac{-b \: \pm \: \sqrt{\Delta}}{2a}}\\ \\ \displaystyle \mathsf{x = \frac{12 \: \pm \: 2\sqrt{57}}{2}}\\ \\ \displaystyle \mathsf{x = 6 \: \pm \: \sqrt{57} }$

Resposta: $\displaystyle \mathsf{x = 6\: \pm \: \sqrt{57}}$