14y^2-3=-19y

Solution for 14y^2-3=-19y equation:

14y^2-3=-19y

We move all terms to the left:

14y^2-3-(-19y)=0

We get rid of parentheses

14y^2+19y-3=0

a = 14; b = 19; c = -3;
Δ = b2-4ac
Δ = 192-4·14·(-3)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-23}{2*14}=\frac{-42}{28}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+23}{2*14}=\frac{4}{28}
=1/7
$