3x(x-6)=10

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

3x(x-6)=10

We move all terms to the left:

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

We multiply parentheses

3x^2-18x-10=0

a = 3; b = -18; c = -10;
Δ = b2-4ac
Δ = -182-4·3·(-10)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*3}=\frac{18-2\sqrt{111}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*3}=\frac{18+2\sqrt{111}}{6}
$