Question

How do you solve 4x squared - 12x = 7 (ALGEBRAICALLY)

Answer 1

$\rm 4x^2-12x=7 \\ \\ 4x^2-12x-7=0 \\ \\ 4x^2+2x-14x-7=0 \\ \\ 2x(2x+1)-7(2x+1)=0 \\ \\ (2x+1)(2x-7)=0 \\ \\ I.~2x+1=0 \longrightarrow \bold{x=-\frac12} \\ ~~~~~~~~~~~~~~or \\ \\ II.~2x-7=0 \longrightarrow \bold{x=\frac72}$

Answer 2

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