-5/9x-2/45x+1/5=-90

Solution for -5/9x-2/45x+1/5=-90 equation:

-5/9x-2/45x+1/5=-90

We move all terms to the left:

-5/9x-2/45x+1/5-(-90)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 45x!=0

x!=0/45

x!=0

x∈R


We add all the numbers together, and all the variables

-5/9x-2/45x+90+1/5=0

We calculate fractions


1620x^2/10125x^2+(-5625x)/10125x^2+(-450x)/10125x^2+90=0

We multiply all the terms by the denominator


1620x^2+(-5625x)+(-450x)+90*10125x^2=0

Wy multiply elements

1620x^2+911250x^2+(-5625x)+(-450x)=0

We get rid of parentheses

1620x^2+911250x^2-5625x-450x=0

We add all the numbers together, and all the variables

912870x^2-6075x=0

a = 912870; b = -6075; c = 0;
Δ = b2-4ac
Δ = -60752-4·912870·0
Δ = 36905625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36905625}=6075$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6075)-6075}{2*912870}=\frac{0}{1825740}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6075)+6075}{2*912870}=\frac{12150}{1825740}
=15/2254
$