X(x+1)=2x+5

Solution for X(x+1)=2x+5 equation:

X(X+1)=2X+5

We move all terms to the left:

X(X+1)-(2X+5)=0

We multiply parentheses

X^2+X-(2X+5)=0

We get rid of parentheses

X^2+X-2X-5=0

We add all the numbers together, and all the variables

X^2-1X-5=0

a = 1; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·1·(-5)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{21}}{2*1}=\frac{1-\sqrt{21}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*1}=\frac{1+\sqrt{21}}{2}
$