5x=1/2x+4

Solution for 5x=1/2x+4 equation:

5x=1/2x+4

We move all terms to the left:

5x-(1/2x+4)=0


Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

5x-1/2x-4=0

We multiply all the terms by the denominator


5x*2x-4*2x-1=0

Wy multiply elements

10x^2-8x-1=0

a = 10; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·10·(-1)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*10}=\frac{8-2\sqrt{26}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*10}=\frac{8+2\sqrt{26}}{20}
$