29x^2-30x-2=0

Solution for 29x^2-30x-2=0 equation:

29x^2-30x-2=0

a = 29; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·29·(-2)
Δ = 1132
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:

$\sqrt{\Delta}=\sqrt{1132}=\sqrt{4*283}=\sqrt{4}*\sqrt{283}=2\sqrt{283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{283}}{2*29}=\frac{30-2\sqrt{283}}{58}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{283}}{2*29}=\frac{30+2\sqrt{283}}{58}
$