-2y^2+12y=11

Solution for -2y^2+12y=11 equation:

-2y^2+12y=11

We move all terms to the left:

-2y^2+12y-(11)=0

a = -2; b = 12; c = -11;
Δ = b2-4ac
Δ = 122-4·(-2)·(-11)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{14}}{2*-2}=\frac{-12-2\sqrt{14}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{14}}{2*-2}=\frac{-12+2\sqrt{14}}{-4}
$