Question

Dada a função $f(x) = 2 x^{2} - 5x - 12$, determine os valores de x para $f(x) = -5$

Answer 1

$f(x)=-5\\\\\\f(x)=2x^2-5x-12\\\\-5=2x^2-5x-12\\\\2x^2-5x-12-5=0\\\\2x^2-5x-17=0\\\\\\x=\dfrac{-b\pm\sqrt{b^2-4\cdot{a}\cdot{c}}}{2\cdot{a}}\\\\\\x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\cdot{2}\cdot{-17}}}{2\cdot(2)}\\\\\\x=\dfrac{5\pm\sqrt{25+136}}{4}\\\\\\x=\dfrac{5\pm\sqrt{161}}{4}\\\\\\\\\boxed{x'=\dfrac{5+\sqrt{161}}{4}}\qquad\qquad\qquad\qquad\boxed{''x=\dfrac{5-\sqrt{161}}{4}}\\\\\\\\\\\boxed{\boxed{f\left(\dfrac{5\pm\sqrt{161}}{4}\right)=-5}}$