-1x+9/5x=1

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

-1x+9/5x=1

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

-5x^2-5x+9=0

a = -5; b = -5; c = +9;
Δ = b2-4ac
Δ = -52-4·(-5)·9
Δ = 205
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{-(-5)-\sqrt{205}}{2*-5}=\frac{5-\sqrt{205}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{205}}{2*-5}=\frac{5+\sqrt{205}}{-10}
$