# Exercise ID254

Algebra → Irrational Equations → Négyzetgyököt tartalmazó egyenletek
[Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 18] [Number of characters: 0]

Solve the following equation.

$\sqrt{9-5x}=\frac{3-x+6}{\sqrt{3-x}}\phantom{\rule{0ex}{0ex}}$ $\sqrt{9-5x}=\frac{9-x}{\sqrt{3-x}}\phantom{\rule{0ex}{0ex}}$ ${\left(\sqrt{9-5x}\right)}^{2}=\frac{{\left(9-x\right)}^{2}}{{\left(\sqrt{3-x}\right)}^{2}}\phantom{\rule{0ex}{0ex}}$ $9-5x=\frac{{\left(9-x\right)}^{2}}{3-x}\phantom{\rule{0ex}{0ex}}$ $\left(9-5x\right)\left(3-x\right)={\left(9-x\right)}^{2}\phantom{\rule{0ex}{0ex}}$ $27-15x-9x+5{x}^{2}=81-18x+{x}^{2}\phantom{\rule{0ex}{0ex}}$ $5{x}^{2}-{x}^{2}-15x-9x+18x+27-81=0\phantom{\rule{0ex}{0ex}}$ $4{x}^{2}-6x-54=0\phantom{\rule{0ex}{0ex}}$ $4{x}^{2}-6x-54=0·/\frac{1}{2}\phantom{\rule{0ex}{0ex}}$ $2{x}^{2}-3x-27=0\phantom{\rule{0ex}{0ex}}$ ${x}_{1,2}=\frac{-\left(-3\right)±\sqrt{{\left(-3\right)}^{2}-4·2·\left(-27\right)}}{2·2}=\frac{3±\sqrt{9+216}}{4}=\frac{3±\sqrt{225}}{4}=\frac{3±15}{4}\phantom{\rule{0ex}{0ex}}$ ${x}_{1}=\frac{9}{2}=3,5>1,8\phantom{\rule{0ex}{0ex}}$ ${x}_{2}=-3<1,8\phantom{\rule{0ex}{0ex}}$ $x=-3\phantom{\rule{0ex}{0ex}}$
$x=-3$