3x+12/2x-10=-1

Solution for 3x+12/2x-10=-1 equation:

3x+12/2x-10=-1

We move all terms to the left:

3x+12/2x-10-(-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

3x+12/2x-9=0

We multiply all the terms by the denominator


3x*2x-9*2x+12=0

Wy multiply elements

6x^2-18x+12=0

a = 6; b = -18; c = +12;
Δ = b2-4ac
Δ = -182-4·6·12
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*6}=\frac{24}{12}
=2
$