3y^2-10y=9=0

Solution for 3y^2-10y=9=0 equation:

3y^2-10y=9=0

We move all terms to the left:

3y^2-10y-(9)=0

a = 3; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·3·(-9)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{13}}{2*3}=\frac{10-4\sqrt{13}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{13}}{2*3}=\frac{10+4\sqrt{13}}{6}
$