2x(3x+2)-5+36x=0

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Solution for 2x(3x+2)-5+36x=0 equation:



2x(3x+2)-5+36x=0
We add all the numbers together, and all the variables
36x+2x(3x+2)-5=0
We multiply parentheses
6x^2+36x+4x-5=0
We add all the numbers together, and all the variables
6x^2+40x-5=0
a = 6; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·6·(-5)
Δ = 1720
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:
$\sqrt{\Delta}=\sqrt{1720}=\sqrt{4*430}=\sqrt{4}*\sqrt{430}=2\sqrt{430}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{430}}{2*6}=\frac{-40-2\sqrt{430}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{430}}{2*6}=\frac{-40+2\sqrt{430}}{12} $

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