2x+16=2/5x

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Solution for 2x+16=2/5x equation:



2x+16=2/5x
We move all terms to the left:
2x+16-(2/5x)=0
Domain of the equation: 5x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-(+2/5x)+16=0
We get rid of parentheses
2x-2/5x+16=0
We multiply all the terms by the denominator
2x*5x+16*5x-2=0
Wy multiply elements
10x^2+80x-2=0
a = 10; b = 80; c = -2;
Δ = b2-4ac
Δ = 802-4·10·(-2)
Δ = 6480
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:
$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*10}=\frac{-80-36\sqrt{5}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*10}=\frac{-80+36\sqrt{5}}{20} $

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