3x-10=6/4x+2

Solution for 3x-10=6/4x+2 equation:

3x-10=6/4x+2

We move all terms to the left:

3x-10-(6/4x+2)=0


Domain of the equation: 4x+2)!=0

x∈R


We get rid of parentheses

3x-6/4x-2-10=0

We multiply all the terms by the denominator


3x*4x-2*4x-10*4x-6=0

Wy multiply elements

12x^2-8x-40x-6=0

We add all the numbers together, and all the variables

12x^2-48x-6=0

a = 12; b = -48; c = -6;
Δ = b2-4ac
Δ = -482-4·12·(-6)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-36\sqrt{2}}{2*12}=\frac{48-36\sqrt{2}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+36\sqrt{2}}{2*12}=\frac{48+36\sqrt{2}}{24}
$