3y^2-78y+250=0

Solution for 3y^2-78y+250=0 equation:

3y^2-78y+250=0

a = 3; b = -78; c = +250;
Δ = b2-4ac
Δ = -782-4·3·250
Δ = 3084
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:

$\sqrt{\Delta}=\sqrt{3084}=\sqrt{4*771}=\sqrt{4}*\sqrt{771}=2\sqrt{771}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{771}}{2*3}=\frac{78-2\sqrt{771}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{771}}{2*3}=\frac{78+2\sqrt{771}}{6}
$