(3x+8)(6x+1)=180

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Solution for (3x+8)(6x+1)=180 equation:



(3x+8)(6x+1)=180
We move all terms to the left:
(3x+8)(6x+1)-(180)=0
We multiply parentheses ..
(+18x^2+3x+48x+8)-180=0
We get rid of parentheses
18x^2+3x+48x+8-180=0
We add all the numbers together, and all the variables
18x^2+51x-172=0
a = 18; b = 51; c = -172;
Δ = b2-4ac
Δ = 512-4·18·(-172)
Δ = 14985
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:
$\sqrt{\Delta}=\sqrt{14985}=\sqrt{81*185}=\sqrt{81}*\sqrt{185}=9\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-9\sqrt{185}}{2*18}=\frac{-51-9\sqrt{185}}{36} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+9\sqrt{185}}{2*18}=\frac{-51+9\sqrt{185}}{36} $

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