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x^2-4x+9x-4=100
We move all terms to the left:
x^2-4x+9x-4-(100)=0
We add all the numbers together, and all the variables
x^2+5x-104=0
a = 1; b = 5; c = -104;
Δ = b2-4ac
Δ = 52-4·1·(-104)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-21}{2*1}=\frac{-26}{2} =-13 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*1}=\frac{16}{2} =8 $
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