x-6/2x+3=1

Solution for x-6/2x+3=1 equation:

x-6/2x+3=1

We move all terms to the left:

x-6/2x+3-(1)=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-6/2x+2=0

We multiply all the terms by the denominator


x*2x+2*2x-6=0

Wy multiply elements

2x^2+4x-6=0

a = 2; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·2·(-6)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*2}=\frac{4}{4}
=1
$