14a^2-5a=1

Solution for 14a^2-5a=1 equation:

14a^2-5a=1

We move all terms to the left:

14a^2-5a-(1)=0

a = 14; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·14·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*14}=\frac{-4}{28}
=-1/7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*14}=\frac{14}{28}
=1/2
$