2y^2+5y=-7y

Solution for 2y^2+5y=-7y equation:

2y^2+5y=-7y

We move all terms to the left:

2y^2+5y-(-7y)=0

We get rid of parentheses

2y^2+5y+7y=0

We add all the numbers together, and all the variables

2y^2+12y=0

a = 2; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·2·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*2}=\frac{-24}{4}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*2}=\frac{0}{4}
=0
$