X(37-x)=210

Solution for X(37-x)=210 equation:

X(37-X)=210

We move all terms to the left:

X(37-X)-(210)=0

We add all the numbers together, and all the variables

X(-1X+37)-210=0

We multiply parentheses

-1X^2+37X-210=0

a = -1; b = 37; c = -210;
Δ = b2-4ac
Δ = 372-4·(-1)·(-210)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-23}{2*-1}=\frac{-60}{-2}
=+30
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+23}{2*-1}=\frac{-14}{-2}
=+7
$