(x-10)(160-2x)=180

Solution for (x-10)(160-2x)=180 equation:

(x-10)(160-2x)=180

We move all terms to the left:

(x-10)(160-2x)-(180)=0

We add all the numbers together, and all the variables

(x-10)(-2x+160)-180=0

We multiply parentheses ..

(-2x^2+160x+20x-1600)-180=0

We get rid of parentheses

-2x^2+160x+20x-1600-180=0

We add all the numbers together, and all the variables

-2x^2+180x-1780=0

a = -2; b = 180; c = -1780;
Δ = b2-4ac
Δ = 1802-4·(-2)·(-1780)
Δ = 18160
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:

$\sqrt{\Delta}=\sqrt{18160}=\sqrt{16*1135}=\sqrt{16}*\sqrt{1135}=4\sqrt{1135}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-4\sqrt{1135}}{2*-2}=\frac{-180-4\sqrt{1135}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+4\sqrt{1135}}{2*-2}=\frac{-180+4\sqrt{1135}}{-4}
$