X(2x+1)=73

Solution for X(2x+1)=73 equation:

X(2X+1)=73

We move all terms to the left:

X(2X+1)-(73)=0

We multiply parentheses

2X^2+X-73=0

a = 2; b = 1; c = -73;
Δ = b2-4ac
Δ = 12-4·2·(-73)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{65}}{2*2}=\frac{-1-3\sqrt{65}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{65}}{2*2}=\frac{-1+3\sqrt{65}}{4}
$