1/5x-9=0.5x-18

Solution for 1/5x-9=0.5x-18 equation:

1/5x-9=0.5x-18

We move all terms to the left:

1/5x-9-(0.5x-18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-0.5x+18-9=0

We multiply all the terms by the denominator


-(0.5x)*5x+18*5x-9*5x+1=0

We add all the numbers together, and all the variables

-(+0.5x)*5x+18*5x-9*5x+1=0

We multiply parentheses

-0x^2+18*5x-9*5x+1=0

Wy multiply elements

-0x^2+90x-45x+1=0

We add all the numbers together, and all the variables

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

a = -1; b = 45; c = +1;
Δ = b2-4ac
Δ = 452-4·(-1)·1
Δ = 2029
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{2029}}{2*-1}=\frac{-45-\sqrt{2029}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2029}}{2*-1}=\frac{-45+\sqrt{2029}}{-2}
$