3x(x-2)-8=10

Solution for 3x(x-2)-8=10 equation:

3x(x-2)-8=10

We move all terms to the left:

3x(x-2)-8-(10)=0

We add all the numbers together, and all the variables

3x(x-2)-18=0

We multiply parentheses

3x^2-6x-18=0

a = 3; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·3·(-18)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{7}}{2*3}=\frac{6-6\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{7}}{2*3}=\frac{6+6\sqrt{7}}{6}
$