(x+400)(x-150)/2=3625

Solution for (x+400)(x-150)/2=3625 equation:

(x+400)(x-150)/2=3625

We move all terms to the left:

(x+400)(x-150)/2-(3625)=0

We multiply parentheses ..

(+x^2-150x+400x-60000)/2-3625=0

We multiply all the terms by the denominator


(+x^2-150x+400x-60000)-3625*2=0

We add all the numbers together, and all the variables

(+x^2-150x+400x-60000)-7250=0

We get rid of parentheses

x^2-150x+400x-60000-7250=0

We add all the numbers together, and all the variables

x^2+250x-67250=0

a = 1; b = 250; c = -67250;
Δ = b2-4ac
Δ = 2502-4·1·(-67250)
Δ = 331500
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:

$\sqrt{\Delta}=\sqrt{331500}=\sqrt{100*3315}=\sqrt{100}*\sqrt{3315}=10\sqrt{3315}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{3315}}{2*1}=\frac{-250-10\sqrt{3315}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{3315}}{2*1}=\frac{-250+10\sqrt{3315}}{2}
$