X(x-3)=1522

Solution for X(x-3)=1522 equation:

X(X-3)=1522

We move all terms to the left:

X(X-3)-(1522)=0

We multiply parentheses

X^2-3X-1522=0

a = 1; b = -3; c = -1522;
Δ = b2-4ac
Δ = -32-4·1·(-1522)
Δ = 6097
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{-(-3)-\sqrt{6097}}{2*1}=\frac{3-\sqrt{6097}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{6097}}{2*1}=\frac{3+\sqrt{6097}}{2}
$