10+0.5x=1/2x-10

Solution for 10+0.5x=1/2x-10 equation:

10+0.5x=1/2x-10

We move all terms to the left:

10+0.5x-(1/2x-10)=0


Domain of the equation: 2x-10)!=0

x∈R


We get rid of parentheses

0.5x-1/2x+10+10=0

We multiply all the terms by the denominator


(0.5x)*2x+10*2x+10*2x-1=0

We add all the numbers together, and all the variables

(+0.5x)*2x+10*2x+10*2x-1=0

We multiply parentheses

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

Wy multiply elements

0x^2+20x+20x-1=0

We add all the numbers together, and all the variables

x^2+40x-1=0

a = 1; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·1·(-1)
Δ = 1604
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:

$\sqrt{\Delta}=\sqrt{1604}=\sqrt{4*401}=\sqrt{4}*\sqrt{401}=2\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{401}}{2*1}=\frac{-40-2\sqrt{401}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{401}}{2*1}=\frac{-40+2\sqrt{401}}{2}
$