X=7+1/2x

Solution for X=7+1/2x equation:

X=7+1/2X

We move all terms to the left:

X-(7+1/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(1/2X+7)=0

We get rid of parentheses

X-1/2X-7=0

We multiply all the terms by the denominator


X*2X-7*2X-1=0

Wy multiply elements

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}
$