Text Solve the following equation: 2x−x2=x−3.\frac{2}{x}-\frac{x}{2} = x-3.x2−2x=x−3. Solution Existence condition: x≠0x\neq 0x=0. Multiply by 2x2x2x: 4−x2=2x(x−3)=2x2−6x ⇒ 3x2−6x−4=0.4 - x^2 = 2x(x-3) = 2x^2 - 6x \;\Rightarrow\; 3x^2 - 6x - 4 = 0.4−x2=2x(x−3)=2x2−6x⇒3x2−6x−4=0. x=6±36+486=6±846=3±213≈2.528 and −0.528.x = \frac{6 \pm \sqrt{36+48}}{6} = \frac{6 \pm \sqrt{84}}{6} = \frac{3 \pm \sqrt{21}}{3} \approx 2.528 \ \text{and}\ -0.528.x=66±36+48=66±84=33±21≈2.528 and −0.528. Both acceptable. x=3±213\boxed{x = \frac{3 \pm \sqrt{21}}{3}}x=33±21