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-5x^2-30x-41=0
a = -5; b = -30; c = -41;
Δ = b2-4ac
Δ = -302-4·(-5)·(-41)
Δ = 80
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{5}}{2*-5}=\frac{30-4\sqrt{5}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{5}}{2*-5}=\frac{30+4\sqrt{5}}{-10} $
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