3x(4x-2)=10x+2

Solution for 3x(4x-2)=10x+2 equation:

3x(4x-2)=10x+2

We move all terms to the left:

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

We multiply parentheses

12x^2-6x-(10x+2)=0

We get rid of parentheses

12x^2-6x-10x-2=0

We add all the numbers together, and all the variables

12x^2-16x-2=0

a = 12; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·12·(-2)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{22}}{2*12}=\frac{16-4\sqrt{22}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{22}}{2*12}=\frac{16+4\sqrt{22}}{24}
$