34x^2+54x+3=0

Solution for 34x^2+54x+3=0 equation:

34x^2+54x+3=0

a = 34; b = 54; c = +3;
Δ = b2-4ac
Δ = 542-4·34·3
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{627}}{2*34}=\frac{-54-2\sqrt{627}}{68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{627}}{2*34}=\frac{-54+2\sqrt{627}}{68}
$