3y+2=y^2+10y+7

Solution for 3y+2=y^2+10y+7 equation:

3y+2=y^2+10y+7

We move all terms to the left:

3y+2-(y^2+10y+7)=0

We get rid of parentheses

-y^2+3y-10y-7+2=0

We add all the numbers together, and all the variables

-1y^2-7y-5=0

a = -1; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·(-1)·(-5)
Δ = 29
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{-(-7)-\sqrt{29}}{2*-1}=\frac{7-\sqrt{29}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*-1}=\frac{7+\sqrt{29}}{-2}
$