x(43.75-x)=300

Solution for x(43.75-x)=300 equation:

x(43.75-x)=300

We move all terms to the left:

x(43.75-x)-(300)=0

We add all the numbers together, and all the variables

x(-1x+43.75)-300=0

We multiply parentheses

-1x^2+43.75x-300=0

a = -1; b = 43.75; c = -300;
Δ = b2-4ac
Δ = 43.752-4·(-1)·(-300)
Δ = 714.0625
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{-(43.75)-\sqrt{714.0625}}{2*-1}=\frac{-43.75-\sqrt{714.0625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43.75)+\sqrt{714.0625}}{2*-1}=\frac{-43.75+\sqrt{714.0625}}{-2}
$