X-2/2x+3=-3

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

X-2/2X+3=-3

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X-2/2X+6=0

We multiply all the terms by the denominator


X*2X+6*2X-2=0

Wy multiply elements

2X^2+12X-2=0

a = 2; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·2·(-2)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*2}=\frac{-12-4\sqrt{10}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*2}=\frac{-12+4\sqrt{10}}{4}
$