15x^2-25x=1

Solution for 15x^2-25x=1 equation:

15x^2-25x=1

We move all terms to the left:

15x^2-25x-(1)=0

a = 15; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·15·(-1)
Δ = 685
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{685}}{2*15}=\frac{25-\sqrt{685}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{685}}{2*15}=\frac{25+\sqrt{685}}{30}
$