3.4-5.1x+1.7x^2=0

Solution for 3.4-5.1x+1.7x^2=0 equation:

3.4-5.1x+1.7x^2=0

a = 1.7; b = -5.1; c = +3.4;
Δ = b2-4ac
Δ = -5.12-4·1.7·3.4
Δ = 2.89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5.1)-\sqrt{2.89}}{2*1.7}=\frac{5.1-\sqrt{2.89}}{3.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.1)+\sqrt{2.89}}{2*1.7}=\frac{5.1+\sqrt{2.89}}{3.4}
$