X(x+2)=4x+5

Solution for X(x+2)=4x+5 equation:

X(X+2)=4X+5

We move all terms to the left:

X(X+2)-(4X+5)=0

We multiply parentheses

X^2+2X-(4X+5)=0

We get rid of parentheses

X^2+2X-4X-5=0

We add all the numbers together, and all the variables

X^2-2X-5=0

a = 1; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·1·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*1}=\frac{2-2\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*1}=\frac{2+2\sqrt{6}}{2}
$