(x+25)(x+50)=1650

Solution for (x+25)(x+50)=1650 equation:

(x+25)(x+50)=1650

We move all terms to the left:

(x+25)(x+50)-(1650)=0

We multiply parentheses ..

(+x^2+50x+25x+1250)-1650=0

We get rid of parentheses

x^2+50x+25x+1250-1650=0

We add all the numbers together, and all the variables

x^2+75x-400=0

a = 1; b = 75; c = -400;
Δ = b2-4ac
Δ = 752-4·1·(-400)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-85}{2*1}=\frac{-160}{2}
=-80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+85}{2*1}=\frac{10}{2}
=5
$