Question

equacão de segundo grau: x²-4=3x/2+6

Answer 1

2X²-3X-20=0
Δ=169
X₁=4
X₂=10/4

Answer 2

vamos lá...

$x^2-4= \frac{3x}{2} +6 \\ \\ mmc=2 \\ \\ 2x^2-8=3x+12 \\ 2x^2-3x-8-12=0 \\ 2x^2-3x-20=0$ 

a=2
b=-3
c=-20

Δ=b²-4ac
Δ=(-3)²-4(2)(-20)
Δ=9+160
Δ=169

$x= \frac{-b\pm \sqrt{\triangle} }{2a}= \frac{-(-3)\pm \sqrt{169} }{4} = \frac{3\pm13}{4} \\ \\ x'= \frac{3+13}{4} =\frac{16}{4} =4 \\ \\ x"= \frac{3-13}{4} =- \frac{10}{4} =-\frac{5}{2} \\ \\ S=\{- \frac{5}{2} ,4\}$