Question 1053554
Use a substitution,
{{{u=cos(theta)}}}
{{{10u^2+9u+2=0}}}
Now just solve it like a quadratic equation,
Factoring,
{{{(5u+2)(2u+1)=0}}}
So then,
{{{5u+2=0}}}
{{{5u=-2}}}
{{{u=-2/5}}}
{{{cos(theta)=-2/5}}}
Use a calculator to solve for the two values.
and,
{{{2u+1=0}}}
{{{2u=-1}}}
{{{u=-1/2}}}
{{{cos(theta)=-1/2}}}
Again use a calculator or from your previous studies,
{{{theta=120}}} and {{{theta=240}}}