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X2-6X=190
We move all terms to the left:
X2-6X-(190)=0
We add all the numbers together, and all the variables
X^2-6X-190=0
a = 1; b = -6; c = -190;
Δ = b2-4ac
Δ = -62-4·1·(-190)
Δ = 796
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{199}}{2*1}=\frac{6-2\sqrt{199}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{199}}{2*1}=\frac{6+2\sqrt{199}}{2} $
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