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:
\(x_{2}=\frac{-b-\sqrt{\Delta}}{2*a}\)
\(x_{2}=\frac{7-\sqrt{1 }}{2}=3\)
\(x^2+12=7x\\ x^2-7x+12=0\\ x^2-3x-4x+12=0\\ x(x-3)-4(x-3)=0\\ (x-4)(x-3)=0\\ x=4 \vee x=3\)