7y(2y-4)=24

Solution for 7y(2y-4)=24 equation:

7y(2y-4)=24

We move all terms to the left:

7y(2y-4)-(24)=0

We multiply parentheses

14y^2-28y-24=0

a = 14; b = -28; c = -24;
Δ = b2-4ac
Δ = -282-4·14·(-24)
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{133}}{2*14}=\frac{28-4\sqrt{133}}{28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{133}}{2*14}=\frac{28+4\sqrt{133}}{28}
$