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

$$x^{2}+12=7*x$$, 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:

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

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

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

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