The general equation of a quadratic equation is given by

The solution to the equation, using the formula method is given by
![\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/kaoalb540qnvy45obw509ttuwfskx00e99.png)
To solve the question, we will apply the formula above to match the options provided
Step1: Match

In this case, a=2, b=-8, c=5
substituting into the formula
we will obtain
![\frac{8\pm\sqrt[]{24}}{4}](https://img.qammunity.org/2023/formulas/mathematics/college/lyy9nb4mtf3qn7r4gsuvnrlkwrxemzqz2b.png)
simplifying further
Upon factoring out 2
We will obtain:
![\frac{4\pm\sqrt[]{6}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/tdl10ss2y3i7pt590nvjlcd8145sk9uixz.png)
Step2: Match

In this case,
a=2, b=-10 and c =-3
substituting into the quadratic formula
we will obtain
![\frac{10\pm2\sqrt[]{19}}{4}](https://img.qammunity.org/2023/formulas/mathematics/college/bq85wiva8to3v4tkk4ai172mu1svvtwhaj.png)
simplifying further
we will obtain
![\frac{5\pm\sqrt[]{19}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/jqmlub6w9mec7l1cy9rjyyn3f0t4ait8xq.png)
Step 3: Match

In this case: a=2, b=-8 and c=-3
substituting into the quadratic formula
we will obtain
![\frac{8\pm2\sqrt[]{22}}{4}](https://img.qammunity.org/2023/formulas/mathematics/college/obu53jcx7ibiyvo3aiuwdgr0nq8hpv0ohl.png)
Simplifying further
we will obtain
![\frac{4+\sqrt[]{22}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/pnyvdxxhdbhgwbpecs5d2baxqbna9w51st.png)
Step 4: Match

In this case: a=2, b=-9 and c =-1
substituting into the quadratic formula
we will obtain
![\frac{9+\sqrt[]{89}}{4}](https://img.qammunity.org/2023/formulas/mathematics/college/yml51v8d0rao8y0ejf4tuu27wn1rrrdpc4.png)
Step 5: Match
