5x^2-24x-41=0

Solution for 5x^2-24x-41=0 equation:

5x^2-24x-41=0

a = 5; b = -24; c = -41;
Δ = b2-4ac
Δ = -242-4·5·(-41)
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{349}}{2*5}=\frac{24-2\sqrt{349}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{349}}{2*5}=\frac{24+2\sqrt{349}}{10}
$