Question

Using the quadratic formula, what is the solution to 2x^2-5x-6=0 ?

Answer 1

$\bf \textit{quadratic formula}\\ \begin{array}{lcclll} 2x^2&-5x&-6&=0\\ \uparrow &\uparrow &\uparrow \\ a&b&c \end{array} \qquad \qquad x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}\\\\ -----------------------------\\\\ x=\cfrac{-(-5)\pm\sqrt{(-5)^2-4(2)(-6)}}{2(2)}\implies x=\cfrac{5\pm\sqrt{25+48}}{4} \\\\\\ x=\cfrac{5\pm\sqrt{73}}{4}\implies x= \begin{cases} \cfrac{5+\sqrt{73}}{4}\\\\ \cfrac{5-\sqrt{73}}{4} \end{cases}$