[tex]3 {x}^{2} + x - 4 = 9[/tex]
[tex]3 {x}^{2} + x - 4 - 9 = 0[/tex]
[tex]3 {x}^{2} + x - 13 = 0[/tex]
[tex]a = 3[/tex]
[tex]b = 1[/tex]
[tex]c = - 13[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {1}^{2} - 4 \times 3 \times ( - 13)[/tex]
[tex]\Delta = 1 + 156[/tex]
[tex]\Delta = 157 >0 =>x_{1}\:\neq\:x_{2}[/tex]
[tex]x_{1,2}=\frac{-b \: \pm \: \sqrt{\Delta}}{2a}[/tex]
[tex]x_{1,2}=\frac{-1\pm\sqrt{157}}{2 \times 3} = \frac{ - 1 \pm \sqrt{157} }{6} [/tex]
[tex]x_{1}=\frac{-1 + \sqrt{157}}{6}[/tex]
[tex]x_{2}=\frac{ - 1 - \sqrt{157}}{6}[/tex]
[tex]9 {x}^{2} - 9x + 2 = 0[/tex]
[tex]a = 9[/tex]
[tex]b = - 9[/tex]
[tex]c = 2[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 9)}^{2} - 4 \times 9 \times 2[/tex]
[tex]\Delta = 81 - 72[/tex]
[tex]\Delta = 9>0=>x_{1}\:\neq\:x_{2}[/tex]
[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a} [/tex]
[tex]x_{1,2}=\frac{-( - 9)\pm\sqrt{9}}{2 \times 9}[/tex]
[tex]x_{1,2}=\frac{9\pm3}{18}[/tex]
[tex]x_{1}=\frac{9 + 3}{18} = \frac{12}{18} = \frac{2}{3} [/tex]
[tex]x_{2}=\frac{9 - 3}{18} = \frac{6}{18} = \frac{1}{3} [/tex]
[tex](x + 2)(2x - 1) + x + 4 = 0[/tex]
[tex]2 {x}^{2} - x + 4x - 2 + x + 4 = 0[/tex]
[tex]2 {x}^{2} + 4x + 2 = 0[/tex]
[tex]a = 2[/tex]
[tex]b = 4[/tex]
[tex]c = 2[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {4}^{2} - 4 \times 2 \times 2[/tex]
[tex]\Delta = 16 - 16[/tex]
[tex]\Delta = 0 \: = > x_{1} = x_{2}[/tex]
[tex]x_{1} = x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 4 + \sqrt{0} }{2 \times 2} = \frac{ - 4 + 0}{4} = - \frac{4}{4} = - 1[/tex]
