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15x(40-x)=180
We move all terms to the left:
15x(40-x)-(180)=0
We add all the numbers together, and all the variables
15x(-1x+40)-180=0
We multiply parentheses
-15x^2+600x-180=0
a = -15; b = 600; c = -180;
Δ = b2-4ac
Δ = 6002-4·(-15)·(-180)
Δ = 349200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{349200}=\sqrt{3600*97}=\sqrt{3600}*\sqrt{97}=60\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-60\sqrt{97}}{2*-15}=\frac{-600-60\sqrt{97}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+60\sqrt{97}}{2*-15}=\frac{-600+60\sqrt{97}}{-30} $
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