[tex] {2x}^{2} + 5x - 3 = 0[/tex]
[tex]a = 2[/tex]
[tex]b = 5[/tex]
[tex]c = - 3[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {5}^{2} - 4 \times 2 \times ( - 3)[/tex]
[tex]\Delta = 25 + 24[/tex]
[tex]\Delta = 49[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}[/tex]
[tex]x_{1,2}=\frac{-5\pm\sqrt{49}}{2 \times 2}[/tex]
[tex]x_{1,2}=\frac{-5\pm7}{4}[/tex]
[tex]x_{1}=\frac{-5 + 7}{4}[/tex]
[tex]x_{1}=\frac{2}{4}[/tex]
[tex]x_{1}=\frac{1}{2}[/tex]
[tex]x_{2}=\frac{-5 - 7}{4}[/tex]
[tex]x_{2}= - \frac{12}{4}[/tex]
[tex]x_{2}= - 3[/tex]
