X=1/2x-2-5-1x

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

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

We move all terms to the left:

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


Domain of the equation: 2X-2-5-1X)!=0

We move all terms containing X to the left, all other terms to the right

2X-1X)!=7

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2X^2+2X^2+14X-1=0

We add all the numbers together, and all the variables

4X^2+14X-1=0

a = 4; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·4·(-1)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{53}}{2*4}=\frac{-14-2\sqrt{53}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{53}}{2*4}=\frac{-14+2\sqrt{53}}{8}
$