X(2x-3)=252

Solution for X(2x-3)=252 equation:

X(2X-3)=252

We move all terms to the left:

X(2X-3)-(252)=0

We multiply parentheses

2X^2-3X-252=0

a = 2; b = -3; c = -252;
Δ = b2-4ac
Δ = -32-4·2·(-252)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*2}=\frac{-42}{4}
=-10+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*2}=\frac{48}{4}
=12
$