(2y+1)(y-14)=0

Solution for (2y+1)(y-14)=0 equation:

(2y+1)(y-14)=0

We multiply parentheses ..

(+2y^2-28y+y-14)=0

We get rid of parentheses

2y^2-28y+y-14=0

We add all the numbers together, and all the variables

2y^2-27y-14=0

a = 2; b = -27; c = -14;
Δ = b2-4ac
Δ = -272-4·2·(-14)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-29}{2*2}=\frac{-2}{4}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+29}{2*2}=\frac{56}{4}
=14
$