(100+w)(150+w)=2(100)(150)

Solution for (100+w)(150+w)=2(100)(150) equation:

(100+w)(150+w)=2(100)(150)

We move all terms to the left:

(100+w)(150+w)-(2(100)(150))=0

determiningTheFunctionDomain
(100+w)(150+w)-2100150=0

We add all the numbers together, and all the variables

(w+100)(w+150)-2100150=0

We multiply parentheses ..

(+w^2+150w+100w+15000)-2100150=0

We get rid of parentheses

w^2+150w+100w+15000-2100150=0

We add all the numbers together, and all the variables

w^2+250w-2085150=0

a = 1; b = 250; c = -2085150;
Δ = b2-4ac
Δ = 2502-4·1·(-2085150)
Δ = 8403100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8403100}=\sqrt{100*84031}=\sqrt{100}*\sqrt{84031}=10\sqrt{84031}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{84031}}{2*1}=\frac{-250-10\sqrt{84031}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{84031}}{2*1}=\frac{-250+10\sqrt{84031}}{2}
$