Question

Como resolve essa equação de segundo grau completa?
x²+5x/2-3/2=0​

Answer 1

Aplicando Bhaskara, temos:

$\Delta~=~\left(\frac{5}{2}\right)^2-4.1.\left(-\frac{3}{2}\right)\\\\\\\Delta~=~\frac{5^2}{2^2}~+~\frac{12}{2}\\\\\\\Delta~=~\frac{1~.~25~+~2~.~12}{4}\\\\\\\boxed{\Delta~=~\frac{49}{4}}\\\\\\\\\\x'~=~\dfrac{-\frac{5}{2}+\sqrt{\frac{49}{4}}}{2~.~1}\\\\\\x'~=~\dfrac{-\frac{5}{2}+\frac{7}{2}}{2}\\\\\\x'~=~\frac{-5+7}{2~.~2}\\\\\\x'~=~\frac{2}{4}\\\\\\\boxed{x'~=~\frac{1}{2}}$

$x''~=~\dfrac{-\frac{5}{2}-\sqrt{\frac{49}{4}}}{2~.~1}\\\\\\x''~=~\dfrac{-\frac{5}{2}-\frac{7}{2}}{2}\\\\\\x''~=~\frac{-5-7}{2~.~2}\\\\\\x''~=~\frac{-12}{4}\\\\\\\boxed{x''~=\,-3}$