(6+0.5*y)*(y+-3.5)=0

Solution for (6+0.5*y)*(y+-3.5)=0 equation:

(6+0.5y)(y+-3.5)=0

We add all the numbers together, and all the variables

(0.5y+6)(y-3.5)=0

We multiply parentheses ..

(+0y^2-0y+6y-21)=0

We get rid of parentheses

0y^2-0y+6y-21=0

We add all the numbers together, and all the variables

y^2+5y-21=0

a = 1; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·1·(-21)
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{109}}{2*1}=\frac{-5-\sqrt{109}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{109}}{2*1}=\frac{-5+\sqrt{109}}{2}
$