(3x+16)(11x-18)=180

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Solution for (3x+16)(11x-18)=180 equation:



(3x+16)(11x-18)=180
We move all terms to the left:
(3x+16)(11x-18)-(180)=0
We multiply parentheses ..
(+33x^2-54x+176x-288)-180=0
We get rid of parentheses
33x^2-54x+176x-288-180=0
We add all the numbers together, and all the variables
33x^2+122x-468=0
a = 33; b = 122; c = -468;
Δ = b2-4ac
Δ = 1222-4·33·(-468)
Δ = 76660
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:
$\sqrt{\Delta}=\sqrt{76660}=\sqrt{4*19165}=\sqrt{4}*\sqrt{19165}=2\sqrt{19165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-2\sqrt{19165}}{2*33}=\frac{-122-2\sqrt{19165}}{66} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+2\sqrt{19165}}{2*33}=\frac{-122+2\sqrt{19165}}{66} $

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