(11x-2)(6x+7)=180

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Solution for (11x-2)(6x+7)=180 equation:



(11x-2)(6x+7)=180
We move all terms to the left:
(11x-2)(6x+7)-(180)=0
We multiply parentheses ..
(+66x^2+77x-12x-14)-180=0
We get rid of parentheses
66x^2+77x-12x-14-180=0
We add all the numbers together, and all the variables
66x^2+65x-194=0
a = 66; b = 65; c = -194;
Δ = b2-4ac
Δ = 652-4·66·(-194)
Δ = 55441
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{-(65)-\sqrt{55441}}{2*66}=\frac{-65-\sqrt{55441}}{132} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+\sqrt{55441}}{2*66}=\frac{-65+\sqrt{55441}}{132} $

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