(1/2y+4)(2y-6)=0

Solution for (1/2y+4)(2y-6)=0 equation:

(1/2y+4)(2y-6)=0


Domain of the equation: 2y+4)(2y-6)!=0

y∈R


We multiply parentheses ..

(+2y^2-6y+8y-24)=0

We get rid of parentheses

2y^2-6y+8y-24=0

We add all the numbers together, and all the variables

2y^2+2y-24=0

a = 2; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·2·(-24)
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{-(2)-14}{2*2}=\frac{-16}{4}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*2}=\frac{12}{4}
=3
$