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-5x^2+224x+5000=0
a = -5; b = 224; c = +5000;
Δ = b2-4ac
Δ = 2242-4·(-5)·5000
Δ = 150176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{150176}=\sqrt{5776*26}=\sqrt{5776}*\sqrt{26}=76\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-76\sqrt{26}}{2*-5}=\frac{-224-76\sqrt{26}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+76\sqrt{26}}{2*-5}=\frac{-224+76\sqrt{26}}{-10} $
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