Question

1) 2x2 + 14x + 2 = 0
2) 2x2 + 1x - 3 = 0

Answer 1

$1)$ Pegando a equação:

$2x^{2}+14x+2=0$

Dividindo-a toda por 2 e resolvendo-a, temos:

$x^{2}+7x+1=0$

$\Delta=b^{2}-4\cdot a\cdot c$
$\Delta=7^{2}-4\cdot1\cdot1$
$\Delta=49-4$
$\Delta=45$

$x=\dfrac{-b\pm\sqrt{\Delta}}{2a}$

$x=\dfrac{-1\pm\sqrt{45}}{2\cdot1}$

$x=\dfrac{-1\pm3\sqrt{5}}{2}$

$S=\{\dfrac{-1-3\sqrt{5}}{2},\;\dfrac{-1+3\sqrt{5}}{2}\}$

$2)$ Resolvendo a equação, temos:

$2x^{2}+1x-3=0$

$\Delta=b^{2}-4\cdot a\cdot c$
$\Delta=1^{2}-4\cdot2\cdot(-3)$
$\Delta=1+24$
$\Delta=25$

$x=\dfrac{-b\pm\sqrt{\Delta}}{2a}$

$x=\dfrac{-1\pm\sqrt{25}}{2\cdot2}$

$x=\dfrac{-1\pm5}{4}$

$\Longrightarrow\;x_{1}=\dfrac{-1+5}{4}=\dfrac{4}{4}=1$

$\Longrightarrow\;x_{2}=\dfrac{-1-5}{4}=\dfrac{-6}{4}=\dfrac{-3}{2}$

$S=\{\dfrac{-3}{2},\;1\}$