# (x-2)(5x+2)=180

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

(x-2)(5x+2)=180
We move all terms to the left:
(x-2)(5x+2)-(180)=0
We multiply parentheses ..
(+5x^2+2x-10x-4)-180=0
We get rid of parentheses
5x^2+2x-10x-4-180=0
We add all the numbers together, and all the variables
5x^2-8x-184=0
a = 5; b = -8; c = -184;Δ = b2-4acΔ = -82-4·5·(-184)Δ = 3744The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$The end solution:
$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{26}}{2*5}=\frac{8-12\sqrt{26}}{10}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{26}}{2*5}=\frac{8+12\sqrt{26}}{10}$

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