x+(x+3)(x+3)=89

Solution for x+(x+3)(x+3)=89 equation:

x+(x+3)(x+3)=89

We move all terms to the left:

x+(x+3)(x+3)-(89)=0

We multiply parentheses ..

(+x^2+3x+3x+9)+x-89=0

We get rid of parentheses

x^2+3x+3x+x+9-89=0

We add all the numbers together, and all the variables

x^2+7x-80=0

a = 1; b = 7; c = -80;
Δ = b2-4ac
Δ = 72-4·1·(-80)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{41}}{2*1}=\frac{-7-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{41}}{2*1}=\frac{-7+3\sqrt{41}}{2}
$