2y^2-34y+21=0

Solution for 2y^2-34y+21=0 equation:

2y^2-34y+21=0

a = 2; b = -34; c = +21;
Δ = b2-4ac
Δ = -342-4·2·21
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{247}}{2*2}=\frac{34-2\sqrt{247}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{247}}{2*2}=\frac{34+2\sqrt{247}}{4}
$