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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