2y(y-2)=7

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

2y(y-2)=7

We move all terms to the left:

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

We multiply parentheses

2y^2-4y-7=0

a = 2; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·2·(-7)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{2}}{2*2}=\frac{4-6\sqrt{2}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{2}}{2*2}=\frac{4+6\sqrt{2}}{4}
$