1/2x+5x=-11

Solution for 1/2x+5x=-11 equation:

1/2x+5x=-11

We move all terms to the left:

1/2x+5x-(-11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/2x+11=0

We multiply all the terms by the denominator


5x*2x+11*2x+1=0

Wy multiply elements

10x^2+22x+1=0

a = 10; b = 22; c = +1;
Δ = b2-4ac
Δ = 222-4·10·1
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{111}}{2*10}=\frac{-22-2\sqrt{111}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{111}}{2*10}=\frac{-22+2\sqrt{111}}{20}
$