0.5(120y-1)y+y=150

Solution for 0.5(120y-1)y+y=150 equation:

0.5(120y-1)y+y=150

We move all terms to the left:

0.5(120y-1)y+y-(150)=0

We add all the numbers together, and all the variables

y+0.5(120y-1)y-150=0

We multiply parentheses

0y^2+y+0y-150=0

We add all the numbers together, and all the variables

y^2+2y-150=0

a = 1; b = 2; c = -150;
Δ = b2-4ac
Δ = 22-4·1·(-150)
Δ = 604
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:

$\sqrt{\Delta}=\sqrt{604}=\sqrt{4*151}=\sqrt{4}*\sqrt{151}=2\sqrt{151}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{151}}{2*1}=\frac{-2-2\sqrt{151}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{151}}{2*1}=\frac{-2+2\sqrt{151}}{2}
$