Сделаем замену 2x² + 7x - 8 = m , тогда 2x² + 7x - 3 = m + 5
m (m + 5) - 6 = 0
m² + 5m - 6 = 0
D = 25 - 4 * 1 * (- 6) = 25 + 24 = 49 = 7²
![m _{1} = \frac{-5+7}{2}=1\\\\m _{2} = \frac{-5-7}{2}=-6](https://tex.z-dn.net/?f=m+_%7B1%7D+%3D+%5Cfrac%7B-5%2B7%7D%7B2%7D%3D1%5C%5C%5C%5Cm+_%7B2%7D+%3D+%5Cfrac%7B-5-7%7D%7B2%7D%3D-6++)
2x² + 7x - 8 = 1 2x² + 7x - 8 = - 6
2x² + 7x - 9 = 0 2x² + 7x - 2 = 0
D = 49 - 4 * 2 * (- 9) = 121 = 11² D = 49 - 4 * 2 * (- 2) = 65
![X _{1} = \frac{-7+11}{4}=1\\\\X _{2}= \frac{-7-11}{4}=- 4,5\\\\X _{3}= \frac{-7+ \sqrt{65} }{4}\\\\X _{4} = \frac{-7- \sqrt{65} }{4}](https://tex.z-dn.net/?f=X+_%7B1%7D+%3D+%5Cfrac%7B-7%2B11%7D%7B4%7D%3D1%5C%5C%5C%5CX+_%7B2%7D%3D+%5Cfrac%7B-7-11%7D%7B4%7D%3D-+4%2C5%5C%5C%5C%5CX+_%7B3%7D%3D+%5Cfrac%7B-7%2B+%5Csqrt%7B65%7D+%7D%7B4%7D%5C%5C%5C%5CX+_%7B4%7D+%3D+%5Cfrac%7B-7-+%5Csqrt%7B65%7D+%7D%7B4%7D++++++)