(5x+20)(x+60)=40

Solution for (5x+20)(x+60)=40 equation:

(5x+20)(x+60)=40

We move all terms to the left:

(5x+20)(x+60)-(40)=0

We multiply parentheses ..

(+5x^2+300x+20x+1200)-40=0

We get rid of parentheses

5x^2+300x+20x+1200-40=0

We add all the numbers together, and all the variables

5x^2+320x+1160=0

a = 5; b = 320; c = +1160;
Δ = b2-4ac
Δ = 3202-4·5·1160
Δ = 79200
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:

$\sqrt{\Delta}=\sqrt{79200}=\sqrt{3600*22}=\sqrt{3600}*\sqrt{22}=60\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320)-60\sqrt{22}}{2*5}=\frac{-320-60\sqrt{22}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320)+60\sqrt{22}}{2*5}=\frac{-320+60\sqrt{22}}{10}
$