36x^2-48x-1=0

Solution for 36x^2-48x-1=0 equation:

36x^2-48x-1=0

a = 36; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·36·(-1)
Δ = 2448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{17}}{2*36}=\frac{48-12\sqrt{17}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{17}}{2*36}=\frac{48+12\sqrt{17}}{72}
$