(X-21)(1+3x)=180

Solution for (X-21)(1+3x)=180 equation:

(X-21)(1+3X)=180

We move all terms to the left:

(X-21)(1+3X)-(180)=0

We add all the numbers together, and all the variables

(X-21)(3X+1)-180=0

We multiply parentheses ..

(+3X^2+X-63X-21)-180=0

We get rid of parentheses

3X^2+X-63X-21-180=0

We add all the numbers together, and all the variables

3X^2-62X-201=0

a = 3; b = -62; c = -201;
Δ = b2-4ac
Δ = -622-4·3·(-201)
Δ = 6256
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:

$\sqrt{\Delta}=\sqrt{6256}=\sqrt{16*391}=\sqrt{16}*\sqrt{391}=4\sqrt{391}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-4\sqrt{391}}{2*3}=\frac{62-4\sqrt{391}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+4\sqrt{391}}{2*3}=\frac{62+4\sqrt{391}}{6}
$