Question

Calculo
5x²-2x+8=160

Answer 1

$\mathtt{5x^2-2x+8=160} \\ \mathtt{5x^2 -2x +8 -160 = 0} \\ \mathtt{5x^2 -2x -152 = 0 } \\ \\ \mathtt{a = 5} \\ \mathtt{b = -2} \\ \mathtt{c = -152}\\\\\mathtt{\Delta = b^2-4~.~a~.~c} \\ \\ \mathtt{\Delta = (-2)^2-4~.~5~.~(-152)} \\ \mathtt{\Delta = 4-20~.~(-152)} \\ \mathtt{\Delta = 4 +3.040} \\\mathtt{\Delta = 3.044} \\ \\ \mathtt{\dfrac{-b +- \sqrt{\Delta}}{2~.~a}}$

$\mathtt{\dfrac{-(-2) +- \sqrt{3.044}}{2~.~5}} \\ \\ \\ \mathtt{\dfrac{2 +- \sqrt{3.044}}{10}} \\ \\ \\ \mathtt{x' =\dfrac{ 2 + \sqrt{3.044} }{10}}(\div2) :~~\mathtt{x'=\dfrac{\sqrt{1.522} +1}{10} (\div2)}~~:~~\boxed{\mathtt{x'= \dfrac{\sqrt{761} +1}{5}}} \\ \\ \\ \mathtt{x'' =\dfrac{2-\sqrt{3.044} }{10} (\div2)} ~:~\mathtt{x" = -\dfrac{\sqrt{1.522} -1}{10}(\div2)} ~:~ \boxed{x=\mathtt{-\dfrac{\sqrt{761} -1}{5}}}$