1/2x+5x=8

Solution for 1/2x+5x=8 equation:

1/2x+5x=8

We move all terms to the left:

1/2x+5x-(8)=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-8=0

We multiply all the terms by the denominator


5x*2x-8*2x+1=0

Wy multiply elements

10x^2-16x+1=0

a = 10; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·10·1
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{-(-16)-6\sqrt{6}}{2*10}=\frac{16-6\sqrt{6}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{6}}{2*10}=\frac{16+6\sqrt{6}}{20}
$