[tex]\text{The zeros of the function:}\ f(x)=0\\\\f(x)=2x^2+8x-3\to2x^2+8x-3=0\ \ \ |+3\\\\2x^2+8x=3\ \ \ |:2\\\\x^2+4x=1.5\\\\x^2+2x\cdot2=1.5\ \ \ \ |+2^2\\\\\underbrace{x^2+2x\cdot2+2^2}_{(a+b)^2=a^2+2ab+b^2}=1.5+2^2\\\\(x+2)^2=5.5\to x+6=\pm\sqrt{5.5}\ \ \ \ |-6\\\\x=-\sqrt{5.5}-6\ \vee\ x=\sqrt{5.5}-6[/tex]
