(6+y)(3y-7)=0

Solution for (6+y)(3y-7)=0 equation:

(6+y)(3y-7)=0

We add all the numbers together, and all the variables

(y+6)(3y-7)=0

We multiply parentheses ..

(+3y^2-7y+18y-42)=0

We get rid of parentheses

3y^2-7y+18y-42=0

We add all the numbers together, and all the variables

3y^2+11y-42=0

a = 3; b = 11; c = -42;
Δ = b2-4ac
Δ = 112-4·3·(-42)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*3}=\frac{-36}{6}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*3}=\frac{14}{6}
=2+1/3
$