(-1/5)x-(1/9)x=-102

Solution for (-1/5)x-(1/9)x=-102 equation:

(-1/5)x-(1/9)x=-102

We move all terms to the left:

(-1/5)x-(1/9)x-(-102)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-1/5)x-(+1/9)x-(-102)=0

We add all the numbers together, and all the variables

(-1/5)x-(+1/9)x+102=0

We multiply parentheses

-1x^2-x^2+102=0

We add all the numbers together, and all the variables

-2x^2+102=0

a = -2; b = 0; c = +102;
Δ = b2-4ac
Δ = 02-4·(-2)·102
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{51}}{2*-2}=\frac{0-4\sqrt{51}}{-4}
=-\frac{4\sqrt{51}}{-4}
=-\frac{\sqrt{51}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{51}}{2*-2}=\frac{0+4\sqrt{51}}{-4}
=\frac{4\sqrt{51}}{-4}
=\frac{\sqrt{51}}{-1}
$