6X^2-82x+120=0

Solution for 6X^2-82x+120=0 equation:

6X^2-82X+120=0

a = 6; b = -82; c = +120;
Δ = b2-4ac
Δ = -822-4·6·120
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-62}{2*6}=\frac{20}{12}
=1+2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+62}{2*6}=\frac{144}{12}
=12
$