5x+1/2x=10

Solution for 5x+1/2x=10 equation:

5x+1/2x=10

We move all terms to the left:

5x+1/2x-(10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


5x*2x-10*2x+1=0

Wy multiply elements

10x^2-20x+1=0

a = 10; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·10·1
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{10}}{2*10}=\frac{20-6\sqrt{10}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{10}}{2*10}=\frac{20+6\sqrt{10}}{20}
$