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x(x+48)=3024
We move all terms to the left:
x(x+48)-(3024)=0
We multiply parentheses
x^2+48x-3024=0
a = 1; b = 48; c = -3024;
Δ = b2-4ac
Δ = 482-4·1·(-3024)
Δ = 14400
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{14400}=120$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-120}{2*1}=\frac{-168}{2} =-84 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+120}{2*1}=\frac{72}{2} =36 $
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