1/2x+5x=165

Solution for 1/2x+5x=165 equation:

1/2x+5x=165

We move all terms to the left:

1/2x+5x-(165)=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-165=0

We multiply all the terms by the denominator


5x*2x-165*2x+1=0

Wy multiply elements

10x^2-330x+1=0

a = 10; b = -330; c = +1;
Δ = b2-4ac
Δ = -3302-4·10·1
Δ = 108860
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:

$\sqrt{\Delta}=\sqrt{108860}=\sqrt{4*27215}=\sqrt{4}*\sqrt{27215}=2\sqrt{27215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-2\sqrt{27215}}{2*10}=\frac{330-2\sqrt{27215}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+2\sqrt{27215}}{2*10}=\frac{330+2\sqrt{27215}}{20}
$