14=6x2-17x

Solution for 14=6x2-17x equation:

14=6x^2-17x

We move all terms to the left:

14-(6x^2-17x)=0

We get rid of parentheses

-6x^2+17x+14=0

a = -6; b = 17; c = +14;
Δ = b2-4ac
Δ = 172-4·(-6)·14
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-25}{2*-6}=\frac{-42}{-12}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*-6}=\frac{8}{-12}
=-2/3
$