(400+20x)(90-2x)=

Solution for (400+20x)(90-2x)= equation:

(400+20x)(90-2x)=

We move all terms to the left:

(400+20x)(90-2x)-()=0

We add all the numbers together, and all the variables

(20x+400)(-2x+90)-()=0

We add all the numbers together, and all the variables

(20x+400)(-2x+90)=0

We multiply parentheses ..

(-40x^2+1800x-800x+36000)=0

We get rid of parentheses

-40x^2+1800x-800x+36000=0

We add all the numbers together, and all the variables

-40x^2+1000x+36000=0

a = -40; b = 1000; c = +36000;
Δ = b2-4ac
Δ = 10002-4·(-40)·36000
Δ = 6760000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6760000}=2600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-2600}{2*-40}=\frac{-3600}{-80}
=+45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+2600}{2*-40}=\frac{1600}{-80}
=-20
$