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x(x+3)=48
We move all terms to the left:
x(x+3)-(48)=0
We multiply parentheses
x^2+3x-48=0
a = 1; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·1·(-48)
Δ = 201
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{-(3)-\sqrt{201}}{2*1}=\frac{-3-\sqrt{201}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*1}=\frac{-3+\sqrt{201}}{2} $
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