9y^2-39y=-25

Solution for 9y^2-39y=-25 equation:

9y^2-39y=-25

We move all terms to the left:

9y^2-39y-(-25)=0

We add all the numbers together, and all the variables

9y^2-39y+25=0

a = 9; b = -39; c = +25;
Δ = b2-4ac
Δ = -392-4·9·25
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{69}}{2*9}=\frac{39-3\sqrt{69}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{69}}{2*9}=\frac{39+3\sqrt{69}}{18}
$