x-5+1/2x+6=13

Solution for x-5+1/2x+6=13 equation:

x-5+1/2x+6=13

We move all terms to the left:

x-5+1/2x+6-(13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-12=0

We multiply all the terms by the denominator


x*2x-12*2x+1=0

Wy multiply elements

2x^2-24x+1=0

a = 2; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·2·1
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{142}}{2*2}=\frac{24-2\sqrt{142}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{142}}{2*2}=\frac{24+2\sqrt{142}}{4}
$