x(0.5x+3)=180

Solution for x(0.5x+3)=180 equation:

x(0.5x+3)=180

We move all terms to the left:

x(0.5x+3)-(180)=0

We multiply parentheses

0x^2+3x-180=0

We add all the numbers together, and all the variables

x^2+3x-180=0

a = 1; b = 3; c = -180;
Δ = b2-4ac
Δ = 32-4·1·(-180)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*1}=\frac{24}{2}
=12
$