Question

Solve using quadratic formula
6x^2-x=2

Answer 1

`6x^2-x=2\implies 6x^2-1x-2=0 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{6}x^2\stackrel{\stackrel{b}{\downarrow }}{-1}x\stackrel{\stackrel{c}{\downarrow }}{-2}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}`

`x = \cfrac{ -(-1) \pm \sqrt { (-1)^2 -4(6)(-2)}}{2(6)}\implies x = \cfrac{1\pm√(1+48)}{12} \\\\\\ x = \cfrac{1\pm√(49)}{12}\implies x = \cfrac{1\pm 7}{12}\implies x = \begin{cases} (8)/(12)\to &(2)/(3)\\[1em] -(6)/(12)\to &-(1)/(2) \end{cases}`