(-11/9)x=-1/5

Solution for (-11/9)x=-1/5 equation:

(-11/9)x=-1/5

We move all terms to the left:

(-11/9)x-(-1/5)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

-11x^2-(-1/5)=0

We get rid of parentheses

-11x^2+1/5=0

We multiply all the terms by the denominator


-11x^2*5+1=0

Wy multiply elements

-55x^2+1=0

a = -55; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-55)·1
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{55}}{2*-55}=\frac{0-2\sqrt{55}}{-110}
=-\frac{2\sqrt{55}}{-110}
=-\frac{\sqrt{55}}{-55}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{55}}{2*-55}=\frac{0+2\sqrt{55}}{-110}
=\frac{2\sqrt{55}}{-110}
=\frac{\sqrt{55}}{-55}
$