Question

Forma de baskhara 2x2+x-3=0

Answer 1

$\large\boxed{\begin{array}{lllllllllll} \rm \: 2x {}^{2} + x - 3 = 0 \\ \\ \Rightarrow \begin{cases} \rm \: a = 2 \\ \rm \: b = 1 \\ \rm \: c = - 3\end{cases} \\ \\ \rm\Delta = b {}^{2} - 4ac \\ \Delta = 1 {}^{2} - 4.2.( - 3) \\ \Delta = 1 + 24 \\ \Delta = 25 \\ \\ \rm \: x = \dfrac{ - b \pm \sqrt{\Delta} }{2a} \\ \\ \rm \: x = \dfrac{ - 1 \pm \sqrt{25} }{2.2} \\ \\ \rm \: x = \dfrac{ - 1 \pm5}{4} \begin{cases} \rm \: x_1 = \dfrac{ - 1 + 5}{4} = \dfrac{4}{4} = \boxed{1} \\ \\ \rm \: x_2 = \dfrac{ - 1 - 5}{ 2} = \dfrac{ - 6}{4} = \boxed{ \dfrac{- 3}{2}}\end{cases}\end{array}}$