Question

6x al cuadrado + 7x +2= 0

Resolución de ecuaciones cuadráticas con la fórmula general

Answer 1

SOLUCIÓN

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                         $Sea\:la\:ecuaci\'on\:cuadr\'atica:\\\\\\ax^2+bx+c=0\\\\\\Por\:f\'ormula\:general\:tenemos\:que:\\\\\\\mathrm{\boxed{x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}}\\\\\\Del\:problema:\\\\\\a=6,b=7,c=2\\\\\\ Entonces\:reemplazamos\\\\\\x_{1,2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x_{1,2}=\dfrac{-(7)\pm \sqrt{(7)^2-[4(6)(2)]}}{2(6)}\\\\\\x_{1,2}=\dfrac{-7\pm \sqrt{49-(48)}}{12}\\\\\\x_{1,2}=\dfrac{-7\pm \sqrt{1}}{12}\\\\\\x_{1,2}=\dfrac{-7\pm1}{12}$

                        $\Rightarrow\:x_{1}=\dfrac{-7+1}{12}\\\\\\x_{1}=\dfrac{-6}{12}\\\\\\\boxed{\boldsymbol{x_{1}=-0.5}}\\\\\\\Rightarrow\:x_{2}=\dfrac{-7-1}{12}\\\\\\x_{2}=\dfrac{-8}{12}\\\\\\\boxed{\boldsymbol{x_{2}=-0.666667}}$