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)=(-b+√(\Delta))/(2*a)`


`x_(1)=(7+√(1 ))/(2)=4`

Second root:


`x_(2)=(-b-√(\Delta))/(2*a)`


`x_(2)=(7-√(1 ))/(2)=3`