3a^2-25a=1

Solution for 3a^2-25a=1 equation:

3a^2-25a=1

We move all terms to the left:

3a^2-25a-(1)=0

a = 3; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·3·(-1)
Δ = 637
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:

$\sqrt{\Delta}=\sqrt{637}=\sqrt{49*13}=\sqrt{49}*\sqrt{13}=7\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-7\sqrt{13}}{2*3}=\frac{25-7\sqrt{13}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+7\sqrt{13}}{2*3}=\frac{25+7\sqrt{13}}{6}
$