24y-28+6y^2=0

Solution for 24y-28+6y^2=0 equation:

24y-28+6y^2=0

a = 6; b = 24; c = -28;
Δ = b2-4ac
Δ = 242-4·6·(-28)
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{78}}{2*6}=\frac{-24-4\sqrt{78}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{78}}{2*6}=\frac{-24+4\sqrt{78}}{12}
$