Question

resolva a equação do 2 grau .. x2 + 9x + 16 = 3x2 -2

Answer 1

$x^{2} +9x+16=3 x^{2} -2\to \\\\\\ x^{2} +9x+16-3 x^{2} +2=0\to \\\\-2 x^{2} +9x+18=0(-1) \\\\ 2 x^{2} -9x-18=0\\\\\\a=2;b=-9;c=-18 \\\\\\ \Delta=b^2-4ac\to \Delta=(-9)^2-4*2*(-18)\to \Delta=81+144\to \Delta=225$



$\\\\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-(-9)+- \sqrt{225} }{2*2} \to x= \frac{9+- 15 }{4} \to \\\\\\ x'= \frac{9+15 }{4} \to x'= \frac{24 }{4}\to x'=6 \\\\\\ x''= \frac{9-15 }{4} \to x''= \frac{-6 }{4}\to x''= \frac{-3 }{2}\\\\\\ S=(\frac{-3 }{2} ;6)$

Answer 2

x² + 9x + 16 = 3x² - 2
x² + 9x + 16 - 3x² + 2 = 0
- 2x² + 9x + 18 = 0 

a = - 2; b = 9; c = 18

Δ = b² - 4ac
Δ = 9² - 4.(-2).18
Δ = 81 + 8.18
Δ = 81 + 144
Δ = 225

x = - b +/- √Δ = - 9 +/- √225
         2a               2.( - 2)

x = - 9 + 15 =  6   (:2)  =  - 3
        - 4         - 4  (:2)        2

x = - 9 - 15 = - 24 = 6
         - 4        - 4

R.: x = - 3/2 e x = 6