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X2-57X-5130=0
We add all the numbers together, and all the variables
X^2-57X-5130=0
a = 1; b = -57; c = -5130;
Δ = b2-4ac
Δ = -572-4·1·(-5130)
Δ = 23769
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{23769}=\sqrt{9*2641}=\sqrt{9}*\sqrt{2641}=3\sqrt{2641}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-3\sqrt{2641}}{2*1}=\frac{57-3\sqrt{2641}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+3\sqrt{2641}}{2*1}=\frac{57+3\sqrt{2641}}{2} $
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