(-4y+5)(-7-3y)=0

Solution for (-4y+5)(-7-3y)=0 equation:

(-4y+5)(-7-3y)=0

We add all the numbers together, and all the variables

(-4y+5)(-3y-7)=0

We multiply parentheses ..

(+12y^2+28y-15y-35)=0

We get rid of parentheses

12y^2+28y-15y-35=0

We add all the numbers together, and all the variables

12y^2+13y-35=0

a = 12; b = 13; c = -35;
Δ = b2-4ac
Δ = 132-4·12·(-35)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-43}{2*12}=\frac{-56}{24}
=-2+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+43}{2*12}=\frac{30}{24}
=1+1/4
$