Question 983694
General solution for formula of quadratic equation is the shortcut for Completing the Square.


Help just on your #1:


{{{3(x^2+(8/3)x+5/3)=0}}}
{{{3(x^2+(8/3)x+(8/6)^2-(8/6)^2+5/3)=0}}}
{{{3((x+8/6)^2-4/3+5/3)=0}}}
{{{3((x+4/3)^2+1/3)=0}}}
{{{highlight_green(3(x+4/3)^2+1=0)}}}-------Same equation but now in standard form.


Finding x
{{{3(x+4/3)^2=-1}}}
{{{(x+4/3)^2=-1/3}}}
{{{x+4/3=0+- sqrt(-1/3)}}}
{{{x=-4/3+- sqrt(-1/3)}}}
Observe the imaginary number.
{{{x=-4/3+- i*sqrt(1/3)}}}
Rationalizing the irrational term,
{{{highlight(x=-4/3+- i*sqrt(3)/3)}}}


You could also use the formula for general solution of a quadratic equation, just substituting the coefficients into the formula.
{{{x=(-8+- sqrt(8^2-4*3*5))/(2*3)}}}
and simplify it.