[tex]2 {x}^{2} = 7x + 1[/tex]
[tex]2 {x}^{2} - 7x - 1 = 0[/tex]
[tex]a = 2[/tex]
[tex]b = - 7[/tex]
[tex]c = - 1[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 7)}^{2} - 4 \times 2 \times ( - 1)[/tex]
[tex]\Delta = 49 + 8[/tex]
[tex]\Delta = 57 > 0 \: = > \exists \: x_{1} \: \neq \: x_{2}[/tex]
[tex]x_{1,2} = \frac{ - b \pm \sqrt{\Delta} }{2a} [/tex]
[tex]x_{1,2} = \frac{ - ( - 7) \pm \sqrt{57} }{2 \times 2} [/tex]
[tex]x_{1,2} = \frac{7 \pm \sqrt{57} }{4} [/tex]
[tex]x_{1} = \frac{7 + \sqrt{57} }{4} [/tex]
[tex]x_{2} = \frac{7 - \sqrt{57} }{4} [/tex]
