8y2=72+y

Solution for 8y2=72+y equation:

8y^2=72+y

We move all terms to the left:

8y^2-(72+y)=0

We add all the numbers together, and all the variables

8y^2-(y+72)=0

We get rid of parentheses

8y^2-y-72=0

We add all the numbers together, and all the variables

8y^2-1y-72=0

a = 8; b = -1; c = -72;
Δ = b2-4ac
Δ = -12-4·8·(-72)
Δ = 2305
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{-(-1)-\sqrt{2305}}{2*8}=\frac{1-\sqrt{2305}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2305}}{2*8}=\frac{1+\sqrt{2305}}{16}
$