X+3=1/2x-3

Solution for X+3=1/2x-3 equation:

X+3=1/2X-3

We move all terms to the left:

X+3-(1/2X-3)=0


Domain of the equation: 2X-3)!=0

X∈R


We get rid of parentheses

X-1/2X+3+3=0

We multiply all the terms by the denominator


X*2X+3*2X+3*2X-1=0

Wy multiply elements

2X^2+6X+6X-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}
$