y^2+6y+15=3-7y

Solution for y^2+6y+15=3-7y equation:

y^2+6y+15=3-7y

We move all terms to the left:

y^2+6y+15-(3-7y)=0

We add all the numbers together, and all the variables

y^2+6y-(-7y+3)+15=0

We get rid of parentheses

y^2+6y+7y-3+15=0

We add all the numbers together, and all the variables

y^2+13y+12=0

a = 1; b = 13; c = +12;
Δ = b2-4ac
Δ = 132-4·1·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*1}=\frac{-24}{2}
=-12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*1}=\frac{-2}{2}
=-1
$