(3+x+18)(3)=x2

Solution for (3+x+18)(3)=x2 equation:

(3+x+18)(3)=x2

We move all terms to the left:

(3+x+18)(3)-(x2)=0

We add all the numbers together, and all the variables

(x+21)3-x2=0

We add all the numbers together, and all the variables

-1x^2+(x+21)3=0

We multiply parentheses

-1x^2+3x+63=0

a = -1; b = 3; c = +63;
Δ = b2-4ac
Δ = 32-4·(-1)·63
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{29}}{2*-1}=\frac{-3-3\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{29}}{2*-1}=\frac{-3+3\sqrt{29}}{-2}
$