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X(1+1)=5X+20
We move all terms to the left:
X(1+1)-(5X+20)=0
We add all the numbers together, and all the variables
X2-(5X+20)=0
We add all the numbers together, and all the variables
X^2-(5X+20)=0
We get rid of parentheses
X^2-5X-20=0
a = 1; b = -5; c = -20;
Δ = b2-4ac
Δ = -52-4·1·(-20)
Δ = 105
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*1}=\frac{5-\sqrt{105}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*1}=\frac{5+\sqrt{105}}{2} $
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