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X(X+2)=11.25
We move all terms to the left:
X(X+2)-(11.25)=0
We add all the numbers together, and all the variables
X(X+2)-11.25=0
We multiply parentheses
X^2+2X-11.25=0
a = 1; b = 2; c = -11.25;
Δ = b2-4ac
Δ = 22-4·1·(-11.25)
Δ = 49
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{49}=7$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-7}{2*1}=\frac{-9}{2} =-4+1/2 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+7}{2*1}=\frac{5}{2} =2+1/2 $
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