(x+121)(x+81)=180

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Solution for (x+121)(x+81)=180 equation:



(x+121)(x+81)=180
We move all terms to the left:
(x+121)(x+81)-(180)=0
We multiply parentheses ..
(+x^2+81x+121x+9801)-180=0
We get rid of parentheses
x^2+81x+121x+9801-180=0
We add all the numbers together, and all the variables
x^2+202x+9621=0
a = 1; b = 202; c = +9621;
Δ = b2-4ac
Δ = 2022-4·1·9621
Δ = 2320
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:
$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(202)-4\sqrt{145}}{2*1}=\frac{-202-4\sqrt{145}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(202)+4\sqrt{145}}{2*1}=\frac{-202+4\sqrt{145}}{2} $

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