[tex]2x^2-5x-3=0\ \ \ \ \ |divide\ both\ isdes\ by\ 2\\\\x^2-2.5x-1.5=0\\\\x^2-2x\times1.25=1.5\\\\x^2-2x\times1.25+1.25^2-1.25^2=1.5\\\\\underbrace{x^2-2x\times1.25+1.25^2}_{use:(a-b)^2=a^2-2ab+b^2}=1.5+1,5625\\\\(x-1.25)^2=3.0625\iff x-1.25=\sqrt{3.0625}\ or\ x-1.25=-\sqrt{3.0625}\\\\x-1.25=1.75\ or\ x-1.25=-1.75\\\\x=1.75+1.25\ or\ x=-1.75+1.25\\\\\boxed{x=3\ or\ x=-0.5}[/tex]