x=-(x+1)(x+1)+8

Solution for x=-(x+1)(x+1)+8 equation:

x=-(x+1)(x+1)+8

We move all terms to the left:

x-(-(x+1)(x+1)+8)=0

We multiply parentheses ..

-(-(+x^2+x+x+1)+8)+x=0


We calculate terms in parentheses: -(-(+x^2+x+x+1)+8), so:

-(+x^2+x+x+1)+8

We get rid of parentheses

-x^2-x-x-1+8

We add all the numbers together, and all the variables

-1x^2-2x+7

Back to the equation:

-(-1x^2-2x+7)


We get rid of parentheses

1x^2+2x+x-7=0

We add all the numbers together, and all the variables

x^2+3x-7=0

a = 1; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·1·(-7)
Δ = 37
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{-(3)-\sqrt{37}}{2*1}=\frac{-3-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{37}}{2*1}=\frac{-3+\sqrt{37}}{2}
$