6y^2-18y=25

Solution for 6y^2-18y=25 equation:

6y^2-18y=25

We move all terms to the left:

6y^2-18y-(25)=0

a = 6; b = -18; c = -25;
Δ = b2-4ac
Δ = -182-4·6·(-25)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{231}}{2*6}=\frac{18-2\sqrt{231}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{231}}{2*6}=\frac{18+2\sqrt{231}}{12}
$