Question

Which is the number, which when squared and added to 12 becomes seven times its value ?

Answer 1

$x^2+12=7x\\ x^2-7x+12=0\\ x^2-3x-4x+12=0\\ x(x-3)-4(x-3)=0\\ (x-4)(x-3)=0\\ x=4 \vee x=3$

Answer 2

$x^{2}+12=7*x$, where x is unknown numer

Now we are moving $7*x$ on left side to obtain quadratic equation:

$x^{2}+12-7*x=0$

Our goal is to find two roots of this equation.

First we are finding delta:

$\Delta =b^{2}-4*a*c$

$\Delta =(-7)^{2}-4*1*12=1$

First root:

$x_{1}=\frac{-b+\sqrt{\Delta}}{2*a}$

$x_{1}=\frac{7+\sqrt{1 }}{2}=4$

Second root:

$x_{2}=\frac{-b-\sqrt{\Delta}}{2*a}$

$x_{2}=\frac{7-\sqrt{1 }}{2}=3$