10y^2-30y=6

Solution for 10y^2-30y=6 equation:

10y^2-30y=6

We move all terms to the left:

10y^2-30y-(6)=0

a = 10; b = -30; c = -6;
Δ = b2-4ac
Δ = -302-4·10·(-6)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{285}}{2*10}=\frac{30-2\sqrt{285}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{285}}{2*10}=\frac{30+2\sqrt{285}}{20}
$