X(2x+1)=136

Solution for X(2x+1)=136 equation:

X(2X+1)=136

We move all terms to the left:

X(2X+1)-(136)=0

We multiply parentheses

2X^2+X-136=0

a = 2; b = 1; c = -136;
Δ = b2-4ac
Δ = 12-4·2·(-136)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-33}{2*2}=\frac{-34}{4}
=-8+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+33}{2*2}=\frac{32}{4}
=8
$