1/5x=2x+9

Solution for 1/5x=2x+9 equation:

1/5x=2x+9

We move all terms to the left:

1/5x-(2x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x-9=0

We multiply all the terms by the denominator


-2x*5x-9*5x+1=0

Wy multiply elements

-10x^2-45x+1=0

a = -10; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·(-10)·1
Δ = 2065
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{-(-45)-\sqrt{2065}}{2*-10}=\frac{45-\sqrt{2065}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2065}}{2*-10}=\frac{45+\sqrt{2065}}{-20}
$