[tex]4x^2-12x=7 \\
4x^2-12x-7=0 \\ \\
a=4 \\ b=-12 \\ c=-7 \\ b^2-4ac=(-12)^2-4 \times 4 \times (-7)=144+112=256 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-12) \pm \sqrt{256}}{2 \times 4}=\frac{12 \pm 16}{2 \times 4}=\frac{4(3 \pm 4)}{2 \times 4}=\frac{3 \pm 4}{2} \\
x=\frac{3-4}{2} \ \lor \ x=\frac{3+4}{2} \\
x=-\frac{1}{2} \ \lor \ x=\frac{7}{2} \\ \\
\boxed{x=-\frac{1}{2} \hbox{ or } x=\frac{7}{2}}[/tex]
