2x+10=1/2x-5

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

2x+10=1/2x-5

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+10x+20x-1=0

We add all the numbers together, and all the variables

4x^2+30x-1=0

a = 4; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·4·(-1)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{229}}{2*4}=\frac{-30-2\sqrt{229}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{229}}{2*4}=\frac{-30+2\sqrt{229}}{8}
$