4x-3=12/2x+2

Solution for 4x-3=12/2x+2 equation:

4x-3=12/2x+2

We move all terms to the left:

4x-3-(12/2x+2)=0


Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

4x-12/2x-2-3=0

We multiply all the terms by the denominator


4x*2x-2*2x-3*2x-12=0

Wy multiply elements

8x^2-4x-6x-12=0

We add all the numbers together, and all the variables

8x^2-10x-12=0

a = 8; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·8·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*8}=\frac{32}{16}
=2
$