X=1/5x-9

Solution for X=1/5x-9 equation:

X=1/5X-9

We move all terms to the left:

X-(1/5X-9)=0


Domain of the equation: 5X-9)!=0

X∈R


We get rid of parentheses

X-1/5X+9=0

We multiply all the terms by the denominator


X*5X+9*5X-1=0

Wy multiply elements

5X^2+45X-1=0

a = 5; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·5·(-1)
Δ = 2045
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{2045}}{2*5}=\frac{-45-\sqrt{2045}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2045}}{2*5}=\frac{-45+\sqrt{2045}}{10}
$