y^2/8=6-y

Solution for y^2/8=6-y equation:

y^2/8=6-y

We move all terms to the left:

y^2/8-(6-y)=0

We add all the numbers together, and all the variables

y^2/8-(-1y+6)=0

We get rid of parentheses

y^2/8+1y-6=0

We multiply all the terms by the denominator


y^2+1y*8-6*8=0

We add all the numbers together, and all the variables

y^2+1y*8-48=0

Wy multiply elements

y^2+8y-48=0

a = 1; b = 8; c = -48;
Δ = b2-4ac
Δ = 82-4·1·(-48)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*1}=\frac{-24}{2}
=-12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*1}=\frac{8}{2}
=4
$