(11x-1)(20x-3)+29=180

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Solution for (11x-1)(20x-3)+29=180 equation:



(11x-1)(20x-3)+29=180
We move all terms to the left:
(11x-1)(20x-3)+29-(180)=0
We add all the numbers together, and all the variables
(11x-1)(20x-3)-151=0
We multiply parentheses ..
(+220x^2-33x-20x+3)-151=0
We get rid of parentheses
220x^2-33x-20x+3-151=0
We add all the numbers together, and all the variables
220x^2-53x-148=0
a = 220; b = -53; c = -148;
Δ = b2-4ac
Δ = -532-4·220·(-148)
Δ = 133049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-\sqrt{133049}}{2*220}=\frac{53-\sqrt{133049}}{440} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{133049}}{2*220}=\frac{53+\sqrt{133049}}{440} $

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