[tex] {(x + 1)}^{2} - 9(x + 6)(x - 1) = 7 {(x + 3)}^{2} - 8[/tex]
[tex] {x}^{2} + 2x + 1 - 9( {x}^{2} - x + 6x - 6) = 7( {x}^{2} + 6x + 9) - 8[/tex]
[tex] {x}^{2} + 2x + 1 - 9( {x}^{2} + 5x - 6) = 7 {x}^{2} + 42x + 63 - 8[/tex]
[tex] {x}^{2} + 2x + 1 - 9 {x}^{2} - 45x + 54 = 7 {x}^{2} + 42x + 63 - 8[/tex]
[tex] {x}^{2} - 9 {x}^{2} - 7 {x}^{2} + 2x - 45x - 42x + 1 + 54 - 63 + 8 = 0[/tex]
[tex] - 15 {x}^{2} - 85x + 0 = 0[/tex]
[tex] - 15 {x}^{2} - 85x = 0[/tex]
[tex]a = - 15[/tex]
[tex]b = - 85[/tex]
[tex]c = 0[/tex]
[tex]\Delta = {b}^{2} - 4ac[/tex]
[tex]\Delta = {( - 85)}^{2} - 4 \times ( - 15) \times 0[/tex]
[tex]\Delta = 7225\:>0\:=>\:\exists\:x_{1}\:\neq\:x_{2}[/tex]
[tex]x_{1,2} = \frac{ - b \pm \sqrt{\Delta} }{2a} = \frac{ - ( - 85) \pm \sqrt{7225} }{2 \times ( - 15)} = \frac{85 \pm85}{ - 30}[/tex]
[tex]x_{1} = \frac{85 + 85}{ -30} = - \frac{85 + 85}{30} = - \frac{170}{30} = - \frac{17}{3} [/tex]
[tex]x_{2} = \frac{85 - 85}{ - 30} = - \frac{85 - 85}{30} = - \frac{0}{30} = 0[/tex]
