4x^2+14x-41=0

Solution for 4x^2+14x-41=0 equation:

4x^2+14x-41=0

a = 4; b = 14; c = -41;
Δ = b2-4ac
Δ = 142-4·4·(-41)
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{213}}{2*4}=\frac{-14-2\sqrt{213}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{213}}{2*4}=\frac{-14+2\sqrt{213}}{8}
$