14x^2+17x=6

Solution for 14x^2+17x=6 equation:

14x^2+17x=6

We move all terms to the left:

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

a = 14; b = 17; c = -6;
Δ = b2-4ac
Δ = 172-4·14·(-6)
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*14}=\frac{-42}{28}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*14}=\frac{8}{28}
=2/7
$