5x^2+24x-1=0

Solution for 5x^2+24x-1=0 equation:

5x^2+24x-1=0

a = 5; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·5·(-1)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{149}}{2*5}=\frac{-24-2\sqrt{149}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{149}}{2*5}=\frac{-24+2\sqrt{149}}{10}
$