[tex]2x ^2 - 5x- 3 \leq 0\\\\a=2, \ \ \ b=-5, \ \ \ c=-3 \\ the \ roots\ : \\ quadratic \ formula:\\\\x_{1} = \frac{-b- \sqrt {b^2 - 4ac} }{ 2a}= \frac{5- \sqrt { (-5)^2 - 4 \cdot 2\cdot (-3)} }{ 2 \cdot 2}= \frac{5- \sqrt { 25 +24} }{ 4}=\\\\=\frac{5- \sqrt {49} }{ 4} =\frac{5- 7 }{ 4}=\frac{-2}{4}=-\frac{1}{2}[/tex]
[tex] x_{2} = \frac{-b+ \sqrt {b^2 - 4ac} }{ 2a}= \frac{5+ \sqrt{49} }{ 4}= \frac{5+7} { 4}= \frac{12} { 4}=3 [/tex]
a > 0 , opens up when
[tex] Answer: \\\\ x \in <-\frac{1}{2},3>[/tex]
