1/5x=2x-3

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Solution for 1/5x=2x-3 equation: 



1/5x=2x-3

We move all terms to the left:

1/5x-(2x-3)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We get rid of parentheses

1/5x-2x+3=0

We multiply all the terms by the denominator


-2x*5x+3*5x+1=0

Wy multiply elements

-10x^2+15x+1=0

a = -10; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-10)·1
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{265}}{2*-10}=\frac{-15-\sqrt{265}}{-20}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{265}}{2*-10}=\frac{-15+\sqrt{265}}{-20}
$

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