(5x+12)(6x-11)=180

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Solution for (5x+12)(6x-11)=180 equation:



(5x+12)(6x-11)=180
We move all terms to the left:
(5x+12)(6x-11)-(180)=0
We multiply parentheses ..
(+30x^2-55x+72x-132)-180=0
We get rid of parentheses
30x^2-55x+72x-132-180=0
We add all the numbers together, and all the variables
30x^2+17x-312=0
a = 30; b = 17; c = -312;
Δ = b2-4ac
Δ = 172-4·30·(-312)
Δ = 37729
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{-(17)-\sqrt{37729}}{2*30}=\frac{-17-\sqrt{37729}}{60} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{37729}}{2*30}=\frac{-17+\sqrt{37729}}{60} $

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