(y+7)(5y-6)=0

Solution for (y+7)(5y-6)=0 equation:

(y+7)(5y-6)=0

We multiply parentheses ..

(+5y^2-6y+35y-42)=0

We get rid of parentheses

5y^2-6y+35y-42=0

We add all the numbers together, and all the variables

5y^2+29y-42=0

a = 5; b = 29; c = -42;
Δ = b2-4ac
Δ = 292-4·5·(-42)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-41}{2*5}=\frac{-70}{10}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+41}{2*5}=\frac{12}{10}
=1+1/5
$