6y^2-38y=32+0

Solution for 6y^2-38y=32+0 equation:

6y^2-38y=32+0

We move all terms to the left:

6y^2-38y-(32+0)=0

We add all the numbers together, and all the variables

6y^2-38y-32=0

a = 6; b = -38; c = -32;
Δ = b2-4ac
Δ = -382-4·6·(-32)
Δ = 2212
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:

$\sqrt{\Delta}=\sqrt{2212}=\sqrt{4*553}=\sqrt{4}*\sqrt{553}=2\sqrt{553}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{553}}{2*6}=\frac{38-2\sqrt{553}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{553}}{2*6}=\frac{38+2\sqrt{553}}{12}
$