(x+50)(x+30)=3000

Solution for (x+50)(x+30)=3000 equation:

(x+50)(x+30)=3000

We move all terms to the left:

(x+50)(x+30)-(3000)=0

We multiply parentheses ..

(+x^2+30x+50x+1500)-3000=0

We get rid of parentheses

x^2+30x+50x+1500-3000=0

We add all the numbers together, and all the variables

x^2+80x-1500=0

a = 1; b = 80; c = -1500;
Δ = b2-4ac
Δ = 802-4·1·(-1500)
Δ = 12400
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:

$\sqrt{\Delta}=\sqrt{12400}=\sqrt{400*31}=\sqrt{400}*\sqrt{31}=20\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{31}}{2*1}=\frac{-80-20\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{31}}{2*1}=\frac{-80+20\sqrt{31}}{2}
$