Answer: [tex]\bold{x=\dfrac{5\pm \sqrt{33}}{2}}[/tex]
Step-by-step explanation:
Move everything to one side so the equation is equal to zero. Then use the quadratic equation to find the solutions:
8x² - 9x - 2 = 7x² - 4x
-7x² + 4x -7x² + 4x
x² - 5x - 2 = 0 ⇒ a = 1, b = -5, c = -2
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2}\\\\\\x=\dfrac{-(-5)\pm \sqrt{(-5)^2-4(1)(-2)}}{2}\\\\\\x=\dfrac{5\pm \sqrt{25+8}}{2}\\\\\\\large\boxed{x=\dfrac{5\pm \sqrt{33}}{2}}[/tex]
