-5/6x-19x=-102

Solution for -5/6x-19x=-102 equation:

-5/6x-19x=-102

We move all terms to the left:

-5/6x-19x-(-102)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-19x-5/6x+102=0

We multiply all the terms by the denominator


-19x*6x+102*6x-5=0

Wy multiply elements

-114x^2+612x-5=0

a = -114; b = 612; c = -5;
Δ = b2-4ac
Δ = 6122-4·(-114)·(-5)
Δ = 372264
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:

$\sqrt{\Delta}=\sqrt{372264}=\sqrt{4*93066}=\sqrt{4}*\sqrt{93066}=2\sqrt{93066}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(612)-2\sqrt{93066}}{2*-114}=\frac{-612-2\sqrt{93066}}{-228}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+2\sqrt{93066}}{2*-114}=\frac{-612+2\sqrt{93066}}{-228}
$