X-4=-1/2x

Solution for X-4=-1/2x equation:

X-4=-1/2X

We move all terms to the left:

X-4-(-1/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We get rid of parentheses

X+1/2X-4=0

We multiply all the terms by the denominator


X*2X-4*2X+1=0

Wy multiply elements

2X^2-8X+1=0

a = 2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·2·1
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{14}}{2*2}=\frac{8-2\sqrt{14}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{14}}{2*2}=\frac{8+2\sqrt{14}}{4}
$