Question

x(x-2)=2(x+6) equação de 2 grau

Answer 1

$x\cdot \left(x-2\right)=2\cdot \left(x+6\right)\\x^2-2x=2x+12\\x^2-2x-2x=12\\x^2-4x=12\\x^2-4x-12=0$

$\rightarrow \:a=1\\\rightarrow \:b=-4\\\rightarrow \:c=-12$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\x=\frac{-\left(-4\right)\pm \sqrt{4^2-\left(4\cdot 1\cdot \left(-12\right)\right)}}{2\cdot 1}\\x=\frac{4\pm \sqrt{16+48}}{2}\\x=\frac{4\pm \sqrt{64}}{2}\\x=\frac{4\pm 8}{2}\\x=2\pm 4\\\\x\left(1\right)=2+4=6\\x\left(2\right)=2-4=-2$

$\boxed{\bold{S=\left(-2,6\right)}}$