(4y-3)(2y+7)=0

Solution for (4y-3)(2y+7)=0 equation:

(4y-3)(2y+7)=0

We multiply parentheses ..

(+8y^2+28y-6y-21)=0

We get rid of parentheses

8y^2+28y-6y-21=0

We add all the numbers together, and all the variables

8y^2+22y-21=0

a = 8; b = 22; c = -21;
Δ = b2-4ac
Δ = 222-4·8·(-21)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-34}{2*8}=\frac{-56}{16}
=-3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+34}{2*8}=\frac{12}{16}
=3/4
$