5x2-40x-333=0

Solution for 5x2-40x-333=0 equation:

5x^2-40x-333=0

a = 5; b = -40; c = -333;
Δ = b2-4ac
Δ = -402-4·5·(-333)
Δ = 8260
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:

$\sqrt{\Delta}=\sqrt{8260}=\sqrt{4*2065}=\sqrt{4}*\sqrt{2065}=2\sqrt{2065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{2065}}{2*5}=\frac{40-2\sqrt{2065}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{2065}}{2*5}=\frac{40+2\sqrt{2065}}{10}
$