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380.8x=136/25x
We move all terms to the left:
380.8x-(136/25x)=0
Domain of the equation: 25x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
380.8x-(+136/25x)=0
We get rid of parentheses
380.8x-136/25x=0
We multiply all the terms by the denominator
(380.8x)*25x-136=0
We add all the numbers together, and all the variables
(+380.8x)*25x-136=0
We multiply parentheses
9500x^2-136=0
a = 9500; b = 0; c = -136;
Δ = b2-4ac
Δ = 02-4·9500·(-136)
Δ = 5168000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5168000}=\sqrt{1600*3230}=\sqrt{1600}*\sqrt{3230}=40\sqrt{3230}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3230}}{2*9500}=\frac{0-40\sqrt{3230}}{19000} =-\frac{40\sqrt{3230}}{19000} =-\frac{\sqrt{3230}}{475} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3230}}{2*9500}=\frac{0+40\sqrt{3230}}{19000} =\frac{40\sqrt{3230}}{19000} =\frac{\sqrt{3230}}{475} $
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