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x(x+1)=3.75
We move all terms to the left:
x(x+1)-(3.75)=0
We add all the numbers together, and all the variables
x(x+1)-3.75=0
We multiply parentheses
x^2+x-3.75=0
a = 1; b = 1; c = -3.75;
Δ = b2-4ac
Δ = 12-4·1·(-3.75)
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-4}{2*1}=\frac{-5}{2} =-2+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+4}{2*1}=\frac{3}{2} =1+1/2 $
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