Question 829491
{{{sqrt(9x-5)=3x^2+2x+3}}}
Square both sides,
{{{9x-5=(3x^2+2x+3)(3x^2+2x+3)}}}
{{{9x-5=3x^2(3x^2+2x+3)+2x(3x^2+2x+3)+3(3x^2+2x+3)}}}
{{{9x-5=(9x^4+6x^3+9x^2)+(6x^3+4x^2+6x)+(9x^2+6x+9)}}}
{{{9x-5=9x^4+12x^3+22x^2+12x+9}}}
{{{9x^4+12x^3+22x^2+3x+14=0}}}
You can factor this equation,
{{{(3x^2-x+2)(3x^2+5x+7)=0}}}
Find solutions for both of those quadratic equations and then verify that they solve the original equation (because of the square root in the original equation).