we know that
The formula to solve a quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex]
In this problem we have
[tex]-8x^{2}+3x+2=0[/tex]
so
[tex]a=-8\\b=3\\c=2[/tex]
substitute in the formula
[tex]x=\frac{-3(+/-)\sqrt{3^{2}-4(-8)(2)}}{2(-8)}[/tex]
[tex]x=\frac{-3(+/-)\sqrt{9+64}}{-16}[/tex]
[tex]x=\frac{-3(+/-)\sqrt{73}}{-16}[/tex]
[tex]x1=\frac{-3+\sqrt{73}}{-16}=\frac{3-\sqrt{73}}{16}[/tex]
[tex]x2=\frac{-3-\sqrt{73}}{-16}=\frac{3+\sqrt{73}}{16}[/tex]
therefore
the answer is
The solution is not correct, there is a sign error under the radical. The radicand should be [tex]73[/tex]
