2x^2-84x+610=0

Solution for 2x^2-84x+610=0 equation:

2x^2-84x+610=0

a = 2; b = -84; c = +610;
Δ = b2-4ac
Δ = -842-4·2·610
Δ = 2176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-8\sqrt{34}}{2*2}=\frac{84-8\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+8\sqrt{34}}{2*2}=\frac{84+8\sqrt{34}}{4}
$