14u^2+11u=9

Solution for 14u^2+11u=9 equation:

14u^2+11u=9

We move all terms to the left:

14u^2+11u-(9)=0

a = 14; b = 11; c = -9;
Δ = b2-4ac
Δ = 112-4·14·(-9)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*14}=\frac{-36}{28}
=-1+2/7
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*14}=\frac{14}{28}
=1/2
$