X(3x+5x+x/5)=164

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Solution for X(3x+5x+x/5)=164 equation:



X(3X+5X+X/5)=164
We move all terms to the left:
X(3X+5X+X/5)-(164)=0
We add all the numbers together, and all the variables
X(+8X+X/5)-164=0
We multiply parentheses
8X^2+X^2-164=0
We add all the numbers together, and all the variables
9X^2-164=0
a = 9; b = 0; c = -164;
Δ = b2-4ac
Δ = 02-4·9·(-164)
Δ = 5904
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:
$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{41}}{2*9}=\frac{0-12\sqrt{41}}{18} =-\frac{12\sqrt{41}}{18} =-\frac{2\sqrt{41}}{3} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{41}}{2*9}=\frac{0+12\sqrt{41}}{18} =\frac{12\sqrt{41}}{18} =\frac{2\sqrt{41}}{3} $

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