78=y^2+5y

Solution for 78=y^2+5y equation:

78=y^2+5y

We move all terms to the left:

78-(y^2+5y)=0

We get rid of parentheses

-y^2-5y+78=0

We add all the numbers together, and all the variables

-1y^2-5y+78=0

a = -1; b = -5; c = +78;
Δ = b2-4ac
Δ = -52-4·(-1)·78
Δ = 337
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{-(-5)-\sqrt{337}}{2*-1}=\frac{5-\sqrt{337}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{337}}{2*-1}=\frac{5+\sqrt{337}}{-2}
$