1x+19/66x=-189

Solution for 1x+19/66x=-189 equation:

1x+19/66x=-189

We move all terms to the left:

1x+19/66x-(-189)=0


Domain of the equation: 66x!=0

x!=0/66

x!=0

x∈R


We add all the numbers together, and all the variables

x+19/66x+189=0

We multiply all the terms by the denominator


x*66x+189*66x+19=0

Wy multiply elements

66x^2+12474x+19=0

a = 66; b = 12474; c = +19;
Δ = b2-4ac
Δ = 124742-4·66·19
Δ = 155595660
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:

$\sqrt{\Delta}=\sqrt{155595660}=\sqrt{4*38898915}=\sqrt{4}*\sqrt{38898915}=2\sqrt{38898915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12474)-2\sqrt{38898915}}{2*66}=\frac{-12474-2\sqrt{38898915}}{132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12474)+2\sqrt{38898915}}{2*66}=\frac{-12474+2\sqrt{38898915}}{132}
$