5a^2-14a+3=0

Solution for 5a^2-14a+3=0 equation:

5a^2-14a+3=0

a = 5; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·5·3
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{34}}{2*5}=\frac{14-2\sqrt{34}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{34}}{2*5}=\frac{14+2\sqrt{34}}{10}
$