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5x^2-10x-890=0
a = 5; b = -10; c = -890;
Δ = b2-4ac
Δ = -102-4·5·(-890)
Δ = 17900
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17900}=\sqrt{100*179}=\sqrt{100}*\sqrt{179}=10\sqrt{179}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{179}}{2*5}=\frac{10-10\sqrt{179}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{179}}{2*5}=\frac{10+10\sqrt{179}}{10} $
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