From {{{7x^2+10x+5}}} we can see that {{{a=7}}}, {{{b=10}}}, and {{{c=5}}}



{{{D=b^2-4ac}}} Start with the discriminant formula.



{{{D=(10)^2-4(7)(5)}}} Plug in {{{a=7}}}, {{{b=10}}}, and {{{c=5}}}



{{{D=100-4(7)(5)}}} Square {{{10}}} to get {{{100}}}



{{{D=100-140}}} Multiply {{{4(7)(5)}}} to get {{{(28)(5)=140}}}



{{{D=-40}}} Subtract {{{140}}} from {{{100}}} to get {{{-40}}}



Since the discriminant is less than zero, this means that there are two complex solutions.



In other words, there are no real solutions.