a^2-14a+3=34

Solution for a^2-14a+3=34 equation:

a^2-14a+3=34

We move all terms to the left:

a^2-14a+3-(34)=0

We add all the numbers together, and all the variables

a^2-14a-31=0

a = 1; b = -14; c = -31;
Δ = b2-4ac
Δ = -142-4·1·(-31)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{5}}{2*1}=\frac{14-8\sqrt{5}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{5}}{2*1}=\frac{14+8\sqrt{5}}{2}
$