y^2=19y+7

Solution for y^2=19y+7 equation:

y^2=19y+7

We move all terms to the left:

y^2-(19y+7)=0

We get rid of parentheses

y^2-19y-7=0

a = 1; b = -19; c = -7;
Δ = b2-4ac
Δ = -192-4·1·(-7)
Δ = 389
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{389}}{2*1}=\frac{19-\sqrt{389}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{389}}{2*1}=\frac{19+\sqrt{389}}{2}
$