(30-y)(y)=176

Solution for (30-y)(y)=176 equation:

(30-y)(y)=176

We move all terms to the left:

(30-y)(y)-(176)=0

We add all the numbers together, and all the variables

(-1y+30)y-176=0

We multiply parentheses

-1y^2+30y-176=0

a = -1; b = 30; c = -176;
Δ = b2-4ac
Δ = 302-4·(-1)·(-176)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-14}{2*-1}=\frac{-44}{-2}
=+22
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+14}{2*-1}=\frac{-16}{-2}
=+8
$