5x^2-8x-133=0

Solution for 5x^2-8x-133=0 equation:

5x^2-8x-133=0

a = 5; b = -8; c = -133;
Δ = b2-4ac
Δ = -82-4·5·(-133)
Δ = 2724
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:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{681}}{2*5}=\frac{8-2\sqrt{681}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{681}}{2*5}=\frac{8+2\sqrt{681}}{10}
$