(6y+5)(7y-8)=0

Solution for (6y+5)(7y-8)=0 equation:

(6y+5)(7y-8)=0

We multiply parentheses ..

(+42y^2-48y+35y-40)=0

We get rid of parentheses

42y^2-48y+35y-40=0

We add all the numbers together, and all the variables

42y^2-13y-40=0

a = 42; b = -13; c = -40;
Δ = b2-4ac
Δ = -132-4·42·(-40)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-83}{2*42}=\frac{-70}{84}
=-5/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+83}{2*42}=\frac{96}{84}
=1+1/7
$