(50-2x)(400+25x)=20400

Solution for (50-2x)(400+25x)=20400 equation:

(50-2x)(400+25x)=20400

We move all terms to the left:

(50-2x)(400+25x)-(20400)=0

We add all the numbers together, and all the variables

(-2x+50)(25x+400)-20400=0

We multiply parentheses ..

(-50x^2-800x+1250x+20000)-20400=0

We get rid of parentheses

-50x^2-800x+1250x+20000-20400=0

We add all the numbers together, and all the variables

-50x^2+450x-400=0

a = -50; b = 450; c = -400;
Δ = b2-4ac
Δ = 4502-4·(-50)·(-400)
Δ = 122500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{122500}=350$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-350}{2*-50}=\frac{-800}{-100}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+350}{2*-50}=\frac{-100}{-100}
=1
$