Решите уравнение........................................................ [latex] \frac{1}{4}*( \frac{1}{x+9}+ \frac{1}{x})= \frac{5}{6}- \frac{3}{x} [/latex]

[latex] \frac{1}{4}\cdot( \frac{1}{x+9}+ \frac{1}{x})= \frac{5}{6}- \frac{3}{x} , \ x \neq 0, \ x \neq 9 \\\ \frac{1}{4}\cdot \frac{x+x+9}{x(x+9)}= \frac{5}{6}- \frac{3}{x} \\\ \frac{1}{4}\cdot \frac{2x+9}{x(x+9)}= \frac{5}{6}- \frac{3}{x} \ / \cdot12x(x+9) \\\ 3(2x+9)=2x(x+9)\cdot5-12(x+9)\cdot3 \\\ 6x+27=10x(x+9)-36(x+9) \\\ 6x+27=10x^2+90x-36x-324 \\\ 10x^2+48x-351=0 \\\ D_1=24^2-10\cdot(-351)=576+3510=4086 \\\ x= \frac{-24\pm \sqrt{4086} }{10} [/latex]