1/2x+9*x=-6

Solution for 1/2x+9*x=-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 = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*18}=\frac{-12-6\sqrt{2}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*18}=\frac{-12+6\sqrt{2}}{36}
$