$\text{a)}{x}^2-7x-8=0$  

$\Delta =49+32=81,\sqrt{\Delta }=9$  

$x=\frac{7-9}{2}=-\frac{2}{2}=-1\text{lub}x=\frac{7+9}{2}=\frac{16}{2}=8$  

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$\text{b)}6x^2+5x-4=0$  

$\Delta =25+96=121,\sqrt{\Delta }=11$  

$x=\frac{-5-11}{12}=\frac{-16}{12}=-\frac{4}{3}\text{lub}x=\frac{-5+11}{12}=\frac{6}{12}=\frac{1}{2}$  

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$\text{c)}-5x^2+3x-7=0$  

$\Delta =9-140<0$  

Δ<0, więc równanie nie ma rozwiązań.

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$\text{d)}4x^2-2x-1=0$  

$\Delta =4+16=20,\sqrt{\Delta }=2\sqrt{5}$  

$x=\frac{2-2\sqrt{5}}{8}=\frac{1-\sqrt{5}}{4}\text{lub}x=\frac{2+2\sqrt{5}}{8}=\frac{1+\sqrt{5}}{4}$  

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$\text{e)}4x^2-12x+9=0$  

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

${\left(2x-3\right)}^2=0$  

$2x-3=0$  

$2x=3\mid :2$  

$x=\frac{3}{2}$  

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$\text{f)}{x}^2+2\sqrt{3}x+3=0$  

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

${\left(x+\sqrt{3}\right)}^2=0$  

$x+\sqrt{3}=0$  

$x=-\sqrt{3}$