(5x+2)(2x+4)=180

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Solution for (5x+2)(2x+4)=180 equation:



(5x+2)(2x+4)=180
We move all terms to the left:
(5x+2)(2x+4)-(180)=0
We multiply parentheses ..
(+10x^2+20x+4x+8)-180=0
We get rid of parentheses
10x^2+20x+4x+8-180=0
We add all the numbers together, and all the variables
10x^2+24x-172=0
a = 10; b = 24; c = -172;
Δ = b2-4ac
Δ = 242-4·10·(-172)
Δ = 7456
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:
$\sqrt{\Delta}=\sqrt{7456}=\sqrt{16*466}=\sqrt{16}*\sqrt{466}=4\sqrt{466}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{466}}{2*10}=\frac{-24-4\sqrt{466}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{466}}{2*10}=\frac{-24+4\sqrt{466}}{20} $

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