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^2-32x-6=0

a = 12; b = -32; c = -6;
Δ = b2-4ac
Δ = -322-4·12·(-6)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{82}}{2*12}=\frac{32-4\sqrt{82}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{82}}{2*12}=\frac{32+4\sqrt{82}}{24}
$