(0.5x+5)*x=300

Solution for (0.5x+5)*x=300 equation:

(0.5x+5)*x=300

We move all terms to the left:

(0.5x+5)*x-(300)=0

We multiply parentheses

0x^2+5x-300=0

We add all the numbers together, and all the variables

x^2+5x-300=0

a = 1; b = 5; c = -300;
Δ = b2-4ac
Δ = 52-4·1·(-300)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*1}=\frac{30}{2}
=15
$