(3x+16)(5x+54)=180

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Solution for (3x+16)(5x+54)=180 equation:



(3x+16)(5x+54)=180
We move all terms to the left:
(3x+16)(5x+54)-(180)=0
We multiply parentheses ..
(+15x^2+162x+80x+864)-180=0
We get rid of parentheses
15x^2+162x+80x+864-180=0
We add all the numbers together, and all the variables
15x^2+242x+684=0
a = 15; b = 242; c = +684;
Δ = b2-4ac
Δ = 2422-4·15·684
Δ = 17524
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:
$\sqrt{\Delta}=\sqrt{17524}=\sqrt{4*4381}=\sqrt{4}*\sqrt{4381}=2\sqrt{4381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(242)-2\sqrt{4381}}{2*15}=\frac{-242-2\sqrt{4381}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(242)+2\sqrt{4381}}{2*15}=\frac{-242+2\sqrt{4381}}{30} $

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