2x^2-34x=914

Solution for 2x^2-34x=914 equation:

2x^2-34x=914

We move all terms to the left:

2x^2-34x-(914)=0

a = 2; b = -34; c = -914;
Δ = b2-4ac
Δ = -342-4·2·(-914)
Δ = 8468
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:

$\sqrt{\Delta}=\sqrt{8468}=\sqrt{4*2117}=\sqrt{4}*\sqrt{2117}=2\sqrt{2117}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{2117}}{2*2}=\frac{34-2\sqrt{2117}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{2117}}{2*2}=\frac{34+2\sqrt{2117}}{4}
$