Verified answer

[tex] -2x^2+3x+5=0[/tex]

[tex] a=-2\quad b=3\quad c=5[/tex]

[tex] \Delta=b^2-4\cdot a\cdot c [/tex]

[tex]\Delta=3^2-4\cdot(-2)\cdot5 [/tex]

[tex] \Delta=9+40 [/tex]

[tex] \Delta=49 [/tex]

[tex]x=\dfrac{-b\pm\sqrt\Delta}{2\cdot a} [/tex]

[tex]x=\dfrac{-3\pm\sqrt{49}}{2\cdot(-2) } [/tex]

[tex] x=\dfrac{-3\pm7}{-4}\begin{cases}x'=\dfrac{-3+7}{-4}=\dfrac{4}{-4}=-1\\\\x''=\dfrac{-3-7}{-4}=\dfrac{-10}{-4}=\dfrac{5}{2}\end{cases}[/tex]

[tex]\red{\boldsymbol{S=\{-1~;~5/2\} }}[/tex]

Resposta:

S= {–1, 5/2}

Explicação passo-a-passo:

[tex] - 2x {}^{2} + 3x + 5 = 0[/tex]

[tex]a = - 2 \: \: \: \: b = 3 \: \: \: \: \: c = 5[/tex]

[tex]delta = b {}^{2} - 4ac[/tex]

[tex]delta = 3 {}^{2} - 4. - 2 \times 5 = 9 + 20 = 49[/tex]

[tex] \sqrt{49} = 7[/tex]

[tex]x1 = \frac{ - 3 + 7}{2. - 2} = \frac{4}{ - 4} = - 1[/tex]

[tex]x2 = \frac{ - 3 - 7}{2. - 2} = \frac{ - 10}{ - 4} = \frac{5}{2} [/tex]