7y(3y-8)=56

Solution for 7y(3y-8)=56 equation:

7y(3y-8)=56

We move all terms to the left:

7y(3y-8)-(56)=0

We multiply parentheses

21y^2-56y-56=0

a = 21; b = -56; c = -56;
Δ = b2-4ac
Δ = -562-4·21·(-56)
Δ = 7840
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:

$\sqrt{\Delta}=\sqrt{7840}=\sqrt{784*10}=\sqrt{784}*\sqrt{10}=28\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-28\sqrt{10}}{2*21}=\frac{56-28\sqrt{10}}{42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+28\sqrt{10}}{2*21}=\frac{56+28\sqrt{10}}{42}
$