x(x+21)=270

Solution for x(x+21)=270 equation:

x(x+21)=270

We move all terms to the left:

x(x+21)-(270)=0

We multiply parentheses

x^2+21x-270=0

a = 1; b = 21; c = -270;
Δ = b2-4ac
Δ = 212-4·1·(-270)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-39}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+39}{2*1}=\frac{18}{2}
=9
$