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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} $
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