10x^2-34x+14=0

Solution for 10x^2-34x+14=0 equation:

10x^2-34x+14=0

a = 10; b = -34; c = +14;
Δ = b2-4ac
Δ = -342-4·10·14
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{149}}{2*10}=\frac{34-2\sqrt{149}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{149}}{2*10}=\frac{34+2\sqrt{149}}{20}
$