(4y-1)(2y+1)=77

Solution for (4y-1)(2y+1)=77 equation:

(4y-1)(2y+1)=77

We move all terms to the left:

(4y-1)(2y+1)-(77)=0

We multiply parentheses ..

(+8y^2+4y-2y-1)-77=0

We get rid of parentheses

8y^2+4y-2y-1-77=0

We add all the numbers together, and all the variables

8y^2+2y-78=0

a = 8; b = 2; c = -78;
Δ = b2-4ac
Δ = 22-4·8·(-78)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-50}{2*8}=\frac{-52}{16}
=-3+1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+50}{2*8}=\frac{48}{16}
=3
$