x(x-3)=270

Solution for x(x-3)=270 equation:

x(x-3)=270

We move all terms to the left:

x(x-3)-(270)=0

We multiply parentheses

x^2-3x-270=0

a = 1; b = -3; c = -270;
Δ = b2-4ac
Δ = -32-4·1·(-270)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-33}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+33}{2*1}=\frac{36}{2}
=18
$