1/5x=2x-27

Solution for 1/5x=2x-27 equation:

1/5x=2x-27

We move all terms to the left:

1/5x-(2x-27)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x+27=0

We multiply all the terms by the denominator


-2x*5x+27*5x+1=0

Wy multiply elements

-10x^2+135x+1=0

a = -10; b = 135; c = +1;
Δ = b2-4ac
Δ = 1352-4·(-10)·1
Δ = 18265
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{-(135)-\sqrt{18265}}{2*-10}=\frac{-135-\sqrt{18265}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+\sqrt{18265}}{2*-10}=\frac{-135+\sqrt{18265}}{-20}
$