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(-5x^2)-41x-30=0
We get rid of parentheses
-5x^2-41x-30=0
a = -5; b = -41; c = -30;
Δ = b2-4ac
Δ = -412-4·(-5)·(-30)
Δ = 1081
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{1081}}{2*-5}=\frac{41-\sqrt{1081}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{1081}}{2*-5}=\frac{41+\sqrt{1081}}{-10} $
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