(5x+20)(x+80)=180

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Solution for (5x+20)(x+80)=180 equation:



(5x+20)(x+80)=180
We move all terms to the left:
(5x+20)(x+80)-(180)=0
We multiply parentheses ..
(+5x^2+400x+20x+1600)-180=0
We get rid of parentheses
5x^2+400x+20x+1600-180=0
We add all the numbers together, and all the variables
5x^2+420x+1420=0
a = 5; b = 420; c = +1420;
Δ = b2-4ac
Δ = 4202-4·5·1420
Δ = 148000
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:
$\sqrt{\Delta}=\sqrt{148000}=\sqrt{400*370}=\sqrt{400}*\sqrt{370}=20\sqrt{370}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-20\sqrt{370}}{2*5}=\frac{-420-20\sqrt{370}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+20\sqrt{370}}{2*5}=\frac{-420+20\sqrt{370}}{10} $

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