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X2-24X+11=0
We add all the numbers together, and all the variables
X^2-24X+11=0
a = 1; b = -24; c = +11;
Δ = b2-4ac
Δ = -242-4·1·11
Δ = 532
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{133}}{2*1}=\frac{24-2\sqrt{133}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{133}}{2*1}=\frac{24+2\sqrt{133}}{2} $
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