X(x-2)+2x+46-5x+40=100

Solution for X(x-2)+2x+46-5x+40=100 equation:

X(X-2)+2X+46-5X+40=100

We move all terms to the left:

X(X-2)+2X+46-5X+40-(100)=0

We add all the numbers together, and all the variables

-3X+X(X-2)-14=0

We multiply parentheses

X^2-3X-2X-14=0

We add all the numbers together, and all the variables

X^2-5X-14=0

a = 1; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*1}=\frac{14}{2}
=7
$