10x=1/2x+5

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

10x=1/2x+5

We move all terms to the left:

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


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

10x-1/2x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-10x-1=0

a = 20; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·20·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*20}=\frac{10-6\sqrt{5}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*20}=\frac{10+6\sqrt{5}}{40}
$