1/2x+20=x-10

Solution for 1/2x+20=x-10 equation:

1/2x+20=x-10

We move all terms to the left:

1/2x+20-(x-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x+10+20=0

We multiply all the terms by the denominator


-x*2x+10*2x+20*2x+1=0

Wy multiply elements

-2x^2+20x+40x+1=0

We add all the numbers together, and all the variables

-2x^2+60x+1=0

a = -2; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-2)·1
Δ = 3608
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:

$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{902}}{2*-2}=\frac{-60-2\sqrt{902}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{902}}{2*-2}=\frac{-60+2\sqrt{902}}{-4}
$