we have
[tex]f(x)=6x^{2}+12x-7[/tex]
Equate the function to zero
[tex]6x^{2}+12x-7=0[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]6x^{2}+12x=7[/tex]
Factor the leading coefficient
[tex]6(x^{2}+2x)=7[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]6(x^{2}+2x+1)=7+6[/tex]
[tex]6(x^{2}+2x+1)=13[/tex]
Rewrite as perfect squares
[tex]6(x+1)^{2}=13[/tex]
[tex](x+1)^{2}=13/6[/tex]
Square root both sides
[tex]x+1=(+/-)\sqrt{\frac{13}{6}}[/tex]
[tex]x=-1(+/-)\sqrt{\frac{13}{6}}[/tex]
[tex]x1=-1+\sqrt{\frac{13}{6}}[/tex]
[tex]x2=-1-\sqrt{\frac{13}{6}}[/tex]
therefore
the answer is
The zeros of the quadratic equation are
[tex]x1=-1+\sqrt{\frac{13}{6}}[/tex]
[tex]x2=-1-\sqrt{\frac{13}{6}}[/tex]
