(x/2)(x-40)=180

Solution for (x/2)(x-40)=180 equation:

(x/2)(x-40)=180

We move all terms to the left:

(x/2)(x-40)-(180)=0


Domain of the equation: 2)(x-40)!=0

x∈R


We add all the numbers together, and all the variables

(+x/2)(x-40)-180=0

We multiply parentheses ..

(+x^2-40x)-180=0

We get rid of parentheses

x^2-40x-180=0

a = 1; b = -40; c = -180;
Δ = b2-4ac
Δ = -402-4·1·(-180)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{145}}{2*1}=\frac{40-4\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{145}}{2*1}=\frac{40+4\sqrt{145}}{2}
$