3y2-42y=120

Solution for 3y2-42y=120 equation:

3y^2-42y=120

We move all terms to the left:

3y^2-42y-(120)=0

a = 3; b = -42; c = -120;
Δ = b2-4ac
Δ = -422-4·3·(-120)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{89}}{2*3}=\frac{42-6\sqrt{89}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{89}}{2*3}=\frac{42+6\sqrt{89}}{6}
$