2(72+0.5y)*y=144

Solution for 2(72+0.5y)*y=144 equation:

2(72+0.5y)*y=144

We move all terms to the left:

2(72+0.5y)*y-(144)=0

We add all the numbers together, and all the variables

2(0.5y+72)*y-144=0

We multiply parentheses

0y^2+144y-144=0

We add all the numbers together, and all the variables

y^2+144y-144=0

a = 1; b = 144; c = -144;
Δ = b2-4ac
Δ = 1442-4·1·(-144)
Δ = 21312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21312}=\sqrt{576*37}=\sqrt{576}*\sqrt{37}=24\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-24\sqrt{37}}{2*1}=\frac{-144-24\sqrt{37}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+24\sqrt{37}}{2*1}=\frac{-144+24\sqrt{37}}{2}
$