Question 666659
the two congruent sides are {{{5x^2+9x-10}}} and {{{4x^2+5x+11}}};

so if two sides congruent, we have

{{{5x^2+9x-10=4x^2+5x+11}}}....solve for {{{x}}}


{{{5x^2-4x^2+9x-5x-10-11=0}}}

{{{x^2+4x-21=0}}}.....use quadratic formula

 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

 {{{x = (-4 +- sqrt( 4^2-4*1*(-21) ))/(2*1) }}} 

 {{{x = (-4 +- sqrt( 16+84 ))/2 }}} 

{{{x = (-4 +- sqrt(100))/2 }}} 

{{{x = (-4 +- 10)/2 }}}.....since side has to be positive, we will look for positive root only 

{{{x = (-4 + 10)/2 }}}

{{{x = 6/2 }}}

{{{highlight(x = 3) }}}