12y^2-16y=5=0

Solution for 12y^2-16y=5=0 equation:

12y^2-16y=5=0

We move all terms to the left:

12y^2-16y-(5)=0

a = 12; b = -16; c = -5;
Δ = b2-4ac
Δ = -162-4·12·(-5)
Δ = 496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*12}=\frac{16-4\sqrt{31}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*12}=\frac{16+4\sqrt{31}}{24}
$