2+2X-1=2x(X+5)=-9

Solution for 2+2X-1=2x(X+5)=-9 equation:

2+2X-1=2X(X+5)=-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(2X(X+5)), so:

2X(X+5)

We multiply parentheses

2X^2+10X

Back to the equation:

-(2X^2+10X)


We get rid of parentheses

-2X^2+2X-10X+1=0

We add all the numbers together, and all the variables

-2X^2-8X+1=0

a = -2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-2)·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*-2}=\frac{8-6\sqrt{2}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*-2}=\frac{8+6\sqrt{2}}{-4}
$