(X-3)(x-7)=3

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Solution for (X-3)(x-7)=3 equation:



(X-3)(X-7)=3
We move all terms to the left:
(X-3)(X-7)-(3)=0
We multiply parentheses ..
(+X^2-7X-3X+21)-3=0
We get rid of parentheses
X^2-7X-3X+21-3=0
We add all the numbers together, and all the variables
X^2-10X+18=0
a = 1; b = -10; c = +18;
Δ = b2-4ac
Δ = -102-4·1·18
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*1}=\frac{10-2\sqrt{7}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*1}=\frac{10+2\sqrt{7}}{2} $

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