b) $3i^2-8i-7=0$

Step 1 ：We are given the quadratic equation in complex numbers: $3i^2-8i-7=0$.

Step 2 ：The general form of a quadratic equation is $a{x}^2+bx+c=0$.

Step 3 ：The solutions to this equation can be found using the quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Step 4 ：In this case, $a=3i$, $b=-8i$, and $c=-7$.

Step 5 ：We substitute these values into the quadratic formula to find the solutions.

Step 6 ：First, we calculate the discriminant $D=b^2-4ac=(4.560867804461815+9.208773812499487j)$.

Step 7 ：Then, we find the first solution $sol1=\frac{-b+\sqrt{D}}{2a}=(-0.20146230208324786+0.7601446340769692j)$.

Step 8 ：Next, we find the second solution $sol2=\frac{-b-\sqrt{D}}{2a}=(2.8681289687499145-0.7601446340769692j)$.

Step 9 ：Finally, we simplify the solutions to get the final answer.

Step 10 ：The solutions to the equation $3i^2-8i-7=0$ are $\boxed{{\displaystyle -0.201+0.760i}}$ and $\boxed{{\displaystyle 2.868-0.760i}}$.