Question 149270
Quickest way is to graph the equations to check for real solutions.
{{{x^2+6x-7}}}
{{{ graph( 300, 300, -10, 10, -10, 10,  x^2+6x-7) }}} 
This can be factored into,
{{{x^2+6x-7=(x+7)(x-1)}}}
x=1 and x=-7 are zeros as you can see.
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{{{z2+z+1=0}}} 
{{{ graph( 300, 300, -10, 10, -10, 10,  x^2+x+1) }}} 
Never crosses the x axis, therefore no real solutions, the solutions are complex.