x(x-45.5)=6000

Solution for x(x-45.5)=6000 equation:

x(x-45.5)=6000

We move all terms to the left:

x(x-45.5)-(6000)=0

We multiply parentheses

x^2-45.5x-6000=0

a = 1; b = -45.5; c = -6000;
Δ = b2-4ac
Δ = -45.52-4·1·(-6000)
Δ = 26070.25
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{-(-45.5)-\sqrt{26070.25}}{2*1}=\frac{45.5-\sqrt{26070.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45.5)+\sqrt{26070.25}}{2*1}=\frac{45.5+\sqrt{26070.25}}{2}
$