7(2y-8)14y+56=0

Solution for 7(2y-8)14y+56=0 equation:

7(2y-8)14y+56=0

We multiply parentheses

196y^2-784y+56=0

a = 196; b = -784; c = +56;
Δ = b2-4ac
Δ = -7842-4·196·56
Δ = 570752
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:

$\sqrt{\Delta}=\sqrt{570752}=\sqrt{3136*182}=\sqrt{3136}*\sqrt{182}=56\sqrt{182}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-784)-56\sqrt{182}}{2*196}=\frac{784-56\sqrt{182}}{392}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-784)+56\sqrt{182}}{2*196}=\frac{784+56\sqrt{182}}{392}
$