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(120+x)2x=18000
We move all terms to the left:
(120+x)2x-(18000)=0
We add all the numbers together, and all the variables
(x+120)2x-18000=0
We multiply parentheses
2x^2+240x-18000=0
a = 2; b = 240; c = -18000;
Δ = b2-4ac
Δ = 2402-4·2·(-18000)
Δ = 201600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{201600}=\sqrt{14400*14}=\sqrt{14400}*\sqrt{14}=120\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-120\sqrt{14}}{2*2}=\frac{-240-120\sqrt{14}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+120\sqrt{14}}{2*2}=\frac{-240+120\sqrt{14}}{4} $
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