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X2-130X+1000=0
We add all the numbers together, and all the variables
X^2-130X+1000=0
a = 1; b = -130; c = +1000;
Δ = b2-4ac
Δ = -1302-4·1·1000
Δ = 12900
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12900}=\sqrt{100*129}=\sqrt{100}*\sqrt{129}=10\sqrt{129}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-10\sqrt{129}}{2*1}=\frac{130-10\sqrt{129}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+10\sqrt{129}}{2*1}=\frac{130+10\sqrt{129}}{2} $
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