x(90-x)=50

Solution for x(90-x)=50 equation:

x(90-x)=50

We move all terms to the left:

x(90-x)-(50)=0

We add all the numbers together, and all the variables

x(-1x+90)-50=0

We multiply parentheses

-1x^2+90x-50=0

a = -1; b = 90; c = -50;
Δ = b2-4ac
Δ = 902-4·(-1)·(-50)
Δ = 7900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7900}=\sqrt{100*79}=\sqrt{100}*\sqrt{79}=10\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{79}}{2*-1}=\frac{-90-10\sqrt{79}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{79}}{2*-1}=\frac{-90+10\sqrt{79}}{-2}
$