X(x-3)+(x-4)=20-x

Solution for X(x-3)+(x-4)=20-x equation:

X(X-3)+(X-4)=20-X

We move all terms to the left:

X(X-3)+(X-4)-(20-X)=0

We add all the numbers together, and all the variables

X(X-3)+(X-4)-(-1X+20)=0

We multiply parentheses

X^2-3X+(X-4)-(-1X+20)=0

We get rid of parentheses

X^2-3X+X+1X-4-20=0

We add all the numbers together, and all the variables

X^2-1X-24=0

a = 1; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·1·(-24)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{97}}{2*1}=\frac{1-\sqrt{97}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*1}=\frac{1+\sqrt{97}}{2}
$