6x(2x-10)=39

Solution for 6x(2x-10)=39 equation:

6x(2x-10)=39

We move all terms to the left:

6x(2x-10)-(39)=0

We multiply parentheses

12x^2-60x-39=0

a = 12; b = -60; c = -39;
Δ = b2-4ac
Δ = -602-4·12·(-39)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{38}}{2*12}=\frac{60-12\sqrt{38}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{38}}{2*12}=\frac{60+12\sqrt{38}}{24}
$