(23-y)*y=120

Solution for (23-y)*y=120 equation:

(23-y)*y=120

We move all terms to the left:

(23-y)*y-(120)=0

We add all the numbers together, and all the variables

(-1y+23)*y-120=0

We multiply parentheses

-1y^2+23y-120=0

a = -1; b = 23; c = -120;
Δ = b2-4ac
Δ = 232-4·(-1)·(-120)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*-1}=\frac{-30}{-2}
=+15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*-1}=\frac{-16}{-2}
=+8
$