10x^2-34x-33=0

Solution for 10x^2-34x-33=0 equation:

10x^2-34x-33=0

a = 10; b = -34; c = -33;
Δ = b2-4ac
Δ = -342-4·10·(-33)
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{619}}{2*10}=\frac{34-2\sqrt{619}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{619}}{2*10}=\frac{34+2\sqrt{619}}{20}
$