(3x+31)(2x-6)=180

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Solution for (3x+31)(2x-6)=180 equation:



(3x+31)(2x-6)=180
We move all terms to the left:
(3x+31)(2x-6)-(180)=0
We multiply parentheses ..
(+6x^2-18x+62x-186)-180=0
We get rid of parentheses
6x^2-18x+62x-186-180=0
We add all the numbers together, and all the variables
6x^2+44x-366=0
a = 6; b = 44; c = -366;
Δ = b2-4ac
Δ = 442-4·6·(-366)
Δ = 10720
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:
$\sqrt{\Delta}=\sqrt{10720}=\sqrt{16*670}=\sqrt{16}*\sqrt{670}=4\sqrt{670}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{670}}{2*6}=\frac{-44-4\sqrt{670}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{670}}{2*6}=\frac{-44+4\sqrt{670}}{12} $

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