6x^2-85x+14=0

Solution for 6x^2-85x+14=0 equation:

6x^2-85x+14=0

a = 6; b = -85; c = +14;
Δ = b2-4ac
Δ = -852-4·6·14
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-83}{2*6}=\frac{2}{12}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+83}{2*6}=\frac{168}{12}
=14
$