(20x-8)(17x+1)=180

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Solution for (20x-8)(17x+1)=180 equation:



(20x-8)(17x+1)=180
We move all terms to the left:
(20x-8)(17x+1)-(180)=0
We multiply parentheses ..
(+340x^2+20x-136x-8)-180=0
We get rid of parentheses
340x^2+20x-136x-8-180=0
We add all the numbers together, and all the variables
340x^2-116x-188=0
a = 340; b = -116; c = -188;
Δ = b2-4ac
Δ = -1162-4·340·(-188)
Δ = 269136
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:
$\sqrt{\Delta}=\sqrt{269136}=\sqrt{144*1869}=\sqrt{144}*\sqrt{1869}=12\sqrt{1869}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-12\sqrt{1869}}{2*340}=\frac{116-12\sqrt{1869}}{680} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+12\sqrt{1869}}{2*340}=\frac{116+12\sqrt{1869}}{680} $

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