0=y^2-6y-47

Solution for 0=y^2-6y-47 equation:

0=y^2-6y-47

We move all terms to the left:

0-(y^2-6y-47)=0

We add all the numbers together, and all the variables

-(y^2-6y-47)=0

We get rid of parentheses

-y^2+6y+47=0

We add all the numbers together, and all the variables

-1y^2+6y+47=0

a = -1; b = 6; c = +47;
Δ = b2-4ac
Δ = 62-4·(-1)·47
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{14}}{2*-1}=\frac{-6-4\sqrt{14}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{14}}{2*-1}=\frac{-6+4\sqrt{14}}{-2}
$