Question

(2x - 3) (x + 4) - 8x = 10

Answer 1

$(2x - 3) * (x + 4) - 8x = 10 \\ \\ 2x^2 + 8x - 3x - 12 - 8x - 10 = 0 \\ \\ 2x^2 + 5x - 12 + 8x - 10 = 0 \\ \\ \\ 2^2 - 3x - 22 = 0$

Resolvendo por Bháskara.

$x = \dfrac{-b \pm \sqrt{b^2 -4*a*c}}{2*a}$

a=2, b=−3, c=−22

Δ=b2−4ac
Δ=(−3)^2−4*(2)*(−22)
Δ=9+176
Δ=185

$x = \dfrac{-b \pm \sqrt{\triangle}}{2*a} \\ \\ \\ x = \dfrac{-(-3) \pm \sqrt{185}}{2*2} \\ \\ \\ x = \dfrac{3 \pm \sqrt{185}}{4} \\ \\ \\ x' = \dfrac{3 + \sqrt{185}}{4} \\ \\ \\ x'' = \dfrac{3 - \sqrt{185}}{4}$

S = {$\dfrac{3 + \sqrt{185}}{4},\ \dfrac{3 - \sqrt{185}}{4}$}