X-2=1/2,x+5

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

X-2=1/2.X+5

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2-10X-4X-1=0

We add all the numbers together, and all the variables

2X^2-14X-1=0

a = 2; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·2·(-1)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{51}}{2*2}=\frac{14-2\sqrt{51}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{51}}{2*2}=\frac{14+2\sqrt{51}}{4}
$