5x^2-30x-1=0

Solution for 5x^2-30x-1=0 equation:

5x^2-30x-1=0

a = 5; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·5·(-1)
Δ = 920
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:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{230}}{2*5}=\frac{30-2\sqrt{230}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{230}}{2*5}=\frac{30+2\sqrt{230}}{10}
$