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0.5x(x+24)=56
We move all terms to the left:
0.5x(x+24)-(56)=0
We multiply parentheses
0x^2+0x-56=0
We add all the numbers together, and all the variables
x^2+x-56=0
a = 1; b = 1; c = -56;
Δ = b2-4ac
Δ = 12-4·1·(-56)
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*1}=\frac{-16}{2} =-8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*1}=\frac{14}{2} =7 $
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