## Elementary Algebra

Step 1: Comparing $5x^{2}+6x+7=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=5$, $b=6$ and $c=7$ 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: $x=\frac{-(6) \pm \sqrt {(6)^{2}-4(5)(7)}}{2(5)}$ Step 4: $x=\frac{-6 \pm \sqrt {36-140}}{10}$ Step 5: $x=\frac{-6 \pm \sqrt {-104}}{10}$ Since there is no way to simplify $\sqrt {-104}$ without introducing complex numbers, there are no real number solutions to the equation.