X(x+.5)=300

Solution for X(x+.5)=300 equation:

X(X+.5)=300

We move all terms to the left:

X(X+.5)-(300)=0

We add all the numbers together, and all the variables

X(X+0.5)-300=0

We multiply parentheses

X^2+0.5X-300=0

a = 1; b = 0.5; c = -300;
Δ = b2-4ac
Δ = 0.52-4·1·(-300)
Δ = 1200.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.5)-\sqrt{1200.25}}{2*1}=\frac{-0.5-\sqrt{1200.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{1200.25}}{2*1}=\frac{-0.5+\sqrt{1200.25}}{2}
$