(y*y+3)-6(7+y)=-47

Solution for (y*y+3)-6(7+y)=-47 equation:

(y*y+3)-6(7+y)=-47

We move all terms to the left:

(y*y+3)-6(7+y)-(-47)=0

We add all the numbers together, and all the variables

(y*y+3)-6(y+7)-(-47)=0

We add all the numbers together, and all the variables

(y*y+3)-6(y+7)+47=0

We multiply parentheses

(y*y+3)-6y-42+47=0

We get rid of parentheses

y*y-6y+3-42+47=0

We add all the numbers together, and all the variables

-6y+y*y+8=0

Wy multiply elements

y^2-6y+8=0

a = 1; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·1·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*1}=\frac{4}{2}
=2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*1}=\frac{8}{2}
=4
$