$\text{a)}2x^2-1=0$  

$2x^2=1\mid :2$  

$x^2=\frac{1}{2}$  

$x^2=\frac{2}{4}$  

$x=\frac{\sqrt{2}}{2}\text{lub}x=-\frac{\sqrt{2}}{2}$  

$x\in \left\{-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right\}$  

---

$\text{b)}9x^2-4=0$  

$9x^2=4\mid :9$  

$x^2=\frac{4}{9}$  

$x=\frac{2}{3}\text{lub}x=-\frac{2}{3}$  

$x\in \left\{-\frac{2}{3},\frac{2}{3}\right\}$  

---

$\text{c)}2x^2+16=0$  

$2x^2=-16\mid :2$  

$x^2=-8<0$  

Równanie jest sprzeczne.

---

$\text{d)}{x}^2-3x=0$  

$x\left(x-3\right)=0$  

$x=0\text{lub}x-3=0$  

$x=0\text{lub}x=3$  

$x\in \left\{0,3\right\}$  

---

$\text{e)}25x^2-3x=0\mid :25$  

$x^2-\frac{3}{25}x=0$  

$x\left(x-\frac{3}{25}\right)=0$  

$x=0\text{lub}x-\frac{3}{25}=0$  

$x=0\text{lub}x=\frac{3}{25}$  

$x\in \left\{0,\frac{3}{25}\right\}$  

---

$\text{f)}\sqrt{3}x-2x^2=0$  

$-2x^2+\sqrt{3}x=0\mid :\left(-2\right)$  

$x^2-\frac{\sqrt{3}}{2}x=0$  

$x\left(x-\frac{\sqrt{3}}{2}\right)=0$  

$x=0\text{lub}x-\frac{\sqrt{3}}{2}=0$  

$x=0\text{lub}x=\frac{\sqrt{3}}{2}$  

$x\in \left\{0,\frac{\sqrt{3}}{2}\right\}$