(x+50)(x+100)=8400

Solution for (x+50)(x+100)=8400 equation:

(x+50)(x+100)=8400

We move all terms to the left:

(x+50)(x+100)-(8400)=0

We multiply parentheses ..

(+x^2+100x+50x+5000)-8400=0

We get rid of parentheses

x^2+100x+50x+5000-8400=0

We add all the numbers together, and all the variables

x^2+150x-3400=0

a = 1; b = 150; c = -3400;
Δ = b2-4ac
Δ = 1502-4·1·(-3400)
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-190}{2*1}=\frac{-340}{2}
=-170
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+190}{2*1}=\frac{40}{2}
=20
$