30x^2-105x-1=0

Solution for 30x^2-105x-1=0 equation:

30x^2-105x-1=0

a = 30; b = -105; c = -1;
Δ = b2-4ac
Δ = -1052-4·30·(-1)
Δ = 11145
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{-(-105)-\sqrt{11145}}{2*30}=\frac{105-\sqrt{11145}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11145}}{2*30}=\frac{105+\sqrt{11145}}{60}
$