X(x-3)-18900=0

Solution for X(x-3)-18900=0 equation:

X(X-3)-18900=0

We multiply parentheses

X^2-3X-18900=0

a = 1; b = -3; c = -18900;
Δ = b2-4ac
Δ = -32-4·1·(-18900)
Δ = 75609
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:

$\sqrt{\Delta}=\sqrt{75609}=\sqrt{9*8401}=\sqrt{9}*\sqrt{8401}=3\sqrt{8401}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{8401}}{2*1}=\frac{3-3\sqrt{8401}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{8401}}{2*1}=\frac{3+3\sqrt{8401}}{2}
$