6x(x-3)-2x(x-1)=10

Solution for 6x(x-3)-2x(x-1)=10 equation:

6x(x-3)-2x(x-1)=10

We move all terms to the left:

6x(x-3)-2x(x-1)-(10)=0

We multiply parentheses

6x^2-2x^2-18x+2x-10=0

We add all the numbers together, and all the variables

4x^2-16x-10=0

a = 4; b = -16; c = -10;
Δ = b2-4ac
Δ = -162-4·4·(-10)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{26}}{2*4}=\frac{16-4\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{26}}{2*4}=\frac{16+4\sqrt{26}}{8}
$