-(5/6)x-(1/9)=-102

Solution for -(5/6)x-(1/9)=-102 equation:

-(5/6)x-(1/9)=-102

We move all terms to the left:

-(5/6)x-(1/9)-(-102)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+5/6)x-(+1/9)-(-102)=0

We add all the numbers together, and all the variables

-(+5/6)x+102-(+1/9)=0

We multiply parentheses

-5x^2+102-(+1/9)=0

We get rid of parentheses

-5x^2+102-1/9=0

We multiply all the terms by the denominator


-5x^2*9-1+102*9=0

We add all the numbers together, and all the variables

-5x^2*9+917=0

Wy multiply elements

-45x^2+917=0

a = -45; b = 0; c = +917;
Δ = b2-4ac
Δ = 02-4·(-45)·917
Δ = 165060
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:

$\sqrt{\Delta}=\sqrt{165060}=\sqrt{36*4585}=\sqrt{36}*\sqrt{4585}=6\sqrt{4585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{4585}}{2*-45}=\frac{0-6\sqrt{4585}}{-90}
=-\frac{6\sqrt{4585}}{-90}
=-\frac{\sqrt{4585}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{4585}}{2*-45}=\frac{0+6\sqrt{4585}}{-90}
=\frac{6\sqrt{4585}}{-90}
=\frac{\sqrt{4585}}{-15}
$