Solve quadratic inequalities with calculations Algebra I

Solve the following inequalities.

2x^2-3x-1 \gt 4

\left( \dfrac{5}{2},\infty \right)

\left(-1,\infty \right)

\left( -1,\dfrac{5}{2} \right)

\left( -\infty,-1 \right)\cup\left( \dfrac{5}{2},\infty \right)

3x^2+6x-7 \leqslant x+1

\left[ -\dfrac{8}{3},\infty \right)

\left(-\infty,1 \right]

\left[ -\dfrac{8}{3},1 \right]

\left(-\infty,-\dfrac{8}{3} \right]\cup\left[ 1,\infty \right)

\left(4x-3\right)\left(x+5\right)\geqslant 3x^{2}+10x-7

\left[ -8,\infty \right)

\left(-\infty,1 \right]

\left[ -8{,}1 \right]

\left(-\infty,-8 \left]\cup\right[ 1,\infty \right)

4 \gt 3x^{2}-2x-4

\left( -\dfrac{4}{3},2 \right)

\left( -\infty,-\dfrac{4}{3} \right)\cup\left(2,\infty\right)

\left( -\dfrac{2}{3},4 \right)

\left( -\infty,-\dfrac{2}{3} \right)\cup\left(4,\infty\right)

x^{2}-9 \lt 0

\left( -3{,}3 \right)

\left( -\infty,-3 \right)\cup\left(3,\infty\right)

\left( -\infty,3 \right)

\left( -\infty,-3 \right)

7x^{2}+x+20 \geqslant 9

The inequality has no solution.

x\geqslant0

x\leqslant0

x\in\mathbb{R}

-5x^{2}+2x-10 \gt 6

x\geqslant0

x\leqslant0

x\in\mathbb{R}

The inequality has no solution.