30y+2y^2=-40

Solution for 30y+2y^2=-40 equation:

30y+2y^2=-40

We move all terms to the left:

30y+2y^2-(-40)=0

We add all the numbers together, and all the variables

2y^2+30y+40=0

a = 2; b = 30; c = +40;
Δ = b2-4ac
Δ = 302-4·2·40
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{145}}{2*2}=\frac{-30-2\sqrt{145}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{145}}{2*2}=\frac{-30+2\sqrt{145}}{4}
$