X^2+(x-7)(x-7)-x=21

Solution for X^2+(x-7)(x-7)-x=21 equation:

X^2+(X-7)(X-7)-X=21

We move all terms to the left:

X^2+(X-7)(X-7)-X-(21)=0

We add all the numbers together, and all the variables

X^2-1X+(X-7)(X-7)-21=0

We multiply parentheses ..

X^2+(+X^2-7X-7X+49)-1X-21=0

We get rid of parentheses

X^2+X^2-7X-7X-1X+49-21=0

We add all the numbers together, and all the variables

2X^2-15X+28=0

a = 2; b = -15; c = +28;
Δ = b2-4ac
Δ = -152-4·2·28
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-1}{2*2}=\frac{14}{4}
=3+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*2}=\frac{16}{4}
=4
$