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x2-3x-97=11
We move all terms to the left:
x2-3x-97-(11)=0
We add all the numbers together, and all the variables
x^2-3x-108=0
a = 1; b = -3; c = -108;
Δ = b2-4ac
Δ = -32-4·1·(-108)
Δ = 441
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*1}=\frac{-18}{2} =-9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*1}=\frac{24}{2} =12 $
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