X(2x+3)=3654

Solution for X(2x+3)=3654 equation:

X(2X+3)=3654

We move all terms to the left:

X(2X+3)-(3654)=0

We multiply parentheses

2X^2+3X-3654=0

a = 2; b = 3; c = -3654;
Δ = b2-4ac
Δ = 32-4·2·(-3654)
Δ = 29241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29241}=171$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-171}{2*2}=\frac{-174}{4}
=-43+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+171}{2*2}=\frac{168}{4}
=42
$