(60-x)(x-40)=50

Solution for (60-x)(x-40)=50 equation:

(60-x)(x-40)=50

We move all terms to the left:

(60-x)(x-40)-(50)=0

We add all the numbers together, and all the variables

(-1x+60)(x-40)-50=0

We multiply parentheses ..

(-1x^2+40x+60x-2400)-50=0

We get rid of parentheses

-1x^2+40x+60x-2400-50=0

We add all the numbers together, and all the variables

-1x^2+100x-2450=0

a = -1; b = 100; c = -2450;
Δ = b2-4ac
Δ = 1002-4·(-1)·(-2450)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{2}}{2*-1}=\frac{-100-10\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{2}}{2*-1}=\frac{-100+10\sqrt{2}}{-2}
$