-1/2x+9x=-6

Solution for -1/2x+9x=-6 equation:

-1/2x+9x=-6

We move all terms to the left:

-1/2x+9x-(-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

9x-1/2x+6=0

We multiply all the terms by the denominator


9x*2x+6*2x-1=0

Wy multiply elements

18x^2+12x-1=0

a = 18; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·18·(-1)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{6}}{2*18}=\frac{-12-6\sqrt{6}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*18}=\frac{-12+6\sqrt{6}}{36}
$