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x*25-x*0.5x=600
We move all terms to the left:
x*25-x*0.5x-(600)=0
Wy multiply elements
0x^2+25x-600=0
We add all the numbers together, and all the variables
x^2+25x-600=0
a = 1; b = 25; c = -600;
Δ = b2-4ac
Δ = 252-4·1·(-600)
Δ = 3025
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{3025}=55$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-55}{2*1}=\frac{-80}{2} =-40 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+55}{2*1}=\frac{30}{2} =15 $
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