(X+1)(2x-1)=252

Solution for (X+1)(2x-1)=252 equation:

(X+1)(2X-1)=252

We move all terms to the left:

(X+1)(2X-1)-(252)=0

We multiply parentheses ..

(+2X^2-1X+2X-1)-252=0

We get rid of parentheses

2X^2-1X+2X-1-252=0

We add all the numbers together, and all the variables

2X^2+X-253=0

a = 2; b = 1; c = -253;
Δ = b2-4ac
Δ = 12-4·2·(-253)
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{-(1)-45}{2*2}=\frac{-46}{4}
=-11+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+45}{2*2}=\frac{44}{4}
=11
$