(y-14)(-4y-1)=0

Solution for (y-14)(-4y-1)=0 equation:

(y-14)(-4y-1)=0

We multiply parentheses ..

(-4y^2-1y+56y+14)=0

We get rid of parentheses

-4y^2-1y+56y+14=0

We add all the numbers together, and all the variables

-4y^2+55y+14=0

a = -4; b = 55; c = +14;
Δ = b2-4ac
Δ = 552-4·(-4)·14
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-57}{2*-4}=\frac{-112}{-8}
=+14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+57}{2*-4}=\frac{2}{-8}
=-1/4
$