4(y-7)6y=-24

Solution for 4(y-7)6y=-24 equation:

4(y-7)6y=-24

We move all terms to the left:

4(y-7)6y-(-24)=0

We add all the numbers together, and all the variables

4(y-7)6y+24=0

We multiply parentheses

24y^2-168y+24=0

a = 24; b = -168; c = +24;
Δ = b2-4ac
Δ = -1682-4·24·24
Δ = 25920
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:

$\sqrt{\Delta}=\sqrt{25920}=\sqrt{5184*5}=\sqrt{5184}*\sqrt{5}=72\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-72\sqrt{5}}{2*24}=\frac{168-72\sqrt{5}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+72\sqrt{5}}{2*24}=\frac{168+72\sqrt{5}}{48}
$