X-5=1/2x+1

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

X-5=1/2X+1

We move all terms to the left:

X-5-(1/2X+1)=0


Domain of the equation: 2X+1)!=0

X∈R


We get rid of parentheses

X-1/2X-1-5=0

We multiply all the terms by the denominator


X*2X-1*2X-5*2X-1=0

Wy multiply elements

2X^2-2X-10X-1=0

We add all the numbers together, and all the variables

2X^2-12X-1=0

a = 2; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·2·(-1)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{38}}{2*2}=\frac{12-2\sqrt{38}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{38}}{2*2}=\frac{12+2\sqrt{38}}{4}
$