(49/5)x=180

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Solution for (49/5)x=180 equation:



(49/5)x=180
We move all terms to the left:
(49/5)x-(180)=0
Domain of the equation: 5)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+49/5)x-180=0
We multiply parentheses
49x^2-180=0
a = 49; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·49·(-180)
Δ = 35280
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:
$\sqrt{\Delta}=\sqrt{35280}=\sqrt{7056*5}=\sqrt{7056}*\sqrt{5}=84\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{5}}{2*49}=\frac{0-84\sqrt{5}}{98} =-\frac{84\sqrt{5}}{98} =-\frac{6\sqrt{5}}{7} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{5}}{2*49}=\frac{0+84\sqrt{5}}{98} =\frac{84\sqrt{5}}{98} =\frac{6\sqrt{5}}{7} $

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