Explanation: To solve the following equation
[tex]9x^2+2x=-3[/tex]We can use the following quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step 1: Let's compare our equation with a generic quadratic equation as follows
As we can see above, first we move -3 from the second term to the first term and when we do that we change its sign to +3. Now we know that a = +9, b = +2 and c = +3.
Step 2: Now all we need to do is to substitute the values of a, b and c into our quadratic formula and solve it to find the roots as follows
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-4\cdot9\cdot3}}{2\cdot9} \\ x=\frac{-2\pm\sqrt[]{4^{}-108}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \end{gathered}[/tex]Final answer: As we can see above inside the square root there is a negative number -104 which means this quadratic equation has no real solutions.
