x-5=1/2x+10

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

x-5=1/2x+10

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-20x-10x-1=0

We add all the numbers together, and all the variables

2x^2-30x-1=0

a = 2; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·2·(-1)
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{227}}{2*2}=\frac{30-2\sqrt{227}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{227}}{2*2}=\frac{30+2\sqrt{227}}{4}
$