(2x+18)(6x+2)=180

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Solution for (2x+18)(6x+2)=180 equation:



(2x+18)(6x+2)=180
We move all terms to the left:
(2x+18)(6x+2)-(180)=0
We multiply parentheses ..
(+12x^2+4x+108x+36)-180=0
We get rid of parentheses
12x^2+4x+108x+36-180=0
We add all the numbers together, and all the variables
12x^2+112x-144=0
a = 12; b = 112; c = -144;
Δ = b2-4ac
Δ = 1122-4·12·(-144)
Δ = 19456
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:
$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-32\sqrt{19}}{2*12}=\frac{-112-32\sqrt{19}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+32\sqrt{19}}{2*12}=\frac{-112+32\sqrt{19}}{24} $

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