Answer
{$-\frac{5}{4},2$}
Work Step by Step
Step 1: Comparing $4x^{2}-3x-10=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$;
$a=4$, $b=-3$ and $c=-10$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt (b^{2}-4ac)}{2a}$
Step 3: Substituting the values of a,b and c in the formula:
$x=\frac{-(-3) \pm \sqrt ((-3)^{2}-4(4)(-10))}{2(4)}$
Step 4: $x=\frac{3 \pm \sqrt (9+160)}{8}$
Step 5: $x=\frac{3 \pm \sqrt (169)}{8}$
Step 6: $x=\frac{3 \pm13}{8}$
Step 7: $x=\frac{3+13}{8}$ or $x=\frac{3-13}{8}$
Step 8: $x=\frac{16}{8}$ or $x=\frac{-10}{8}$
Step 9: $x=2$ or $x=-\frac{5}{4}$
Step 10: Therefore, the solution set is {$-\frac{5}{4},2$}.
