2x-6=1/2x+5

Solution for 2x-6=1/2x+5 equation:

2x-6=1/2x+5

We move all terms to the left:

2x-6-(1/2x+5)=0


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

x∈R


We get rid of parentheses

2x-1/2x-5-6=0

We multiply all the terms by the denominator


2x*2x-5*2x-6*2x-1=0

Wy multiply elements

4x^2-10x-12x-1=0

We add all the numbers together, and all the variables

4x^2-22x-1=0

a = 4; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·4·(-1)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10\sqrt{5}}{2*4}=\frac{22-10\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10\sqrt{5}}{2*4}=\frac{22+10\sqrt{5}}{8}
$