(7y-4)(-2y+5)=0

Solution for (7y-4)(-2y+5)=0 equation:

(7y-4)(-2y+5)=0

We multiply parentheses ..

(-14y^2+35y+8y-20)=0

We get rid of parentheses

-14y^2+35y+8y-20=0

We add all the numbers together, and all the variables

-14y^2+43y-20=0

a = -14; b = 43; c = -20;
Δ = b2-4ac
Δ = 432-4·(-14)·(-20)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-27}{2*-14}=\frac{-70}{-28}
=2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+27}{2*-14}=\frac{-16}{-28}
=4/7
$