1-34x+37x^2=0

Solution for 1-34x+37x^2=0 equation:

1-34x+37x^2=0

a = 37; b = -34; c = +1;
Δ = b2-4ac
Δ = -342-4·37·1
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-12\sqrt{7}}{2*37}=\frac{34-12\sqrt{7}}{74}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+12\sqrt{7}}{2*37}=\frac{34+12\sqrt{7}}{74}
$