(2x+60)(2x+40)=3000

Solution for (2x+60)(2x+40)=3000 equation:

(2x+60)(2x+40)=3000

We move all terms to the left:

(2x+60)(2x+40)-(3000)=0

We multiply parentheses ..

(+4x^2+80x+120x+2400)-3000=0

We get rid of parentheses

4x^2+80x+120x+2400-3000=0

We add all the numbers together, and all the variables

4x^2+200x-600=0

a = 4; b = 200; c = -600;
Δ = b2-4ac
Δ = 2002-4·4·(-600)
Δ = 49600
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:

$\sqrt{\Delta}=\sqrt{49600}=\sqrt{1600*31}=\sqrt{1600}*\sqrt{31}=40\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{31}}{2*4}=\frac{-200-40\sqrt{31}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{31}}{2*4}=\frac{-200+40\sqrt{31}}{8}
$