(4/7)x+(1/3)x=57

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Solution for (4/7)x+(1/3)x=57 equation:



(4/7)x+(1/3)x=57
We move all terms to the left:
(4/7)x+(1/3)x-(57)=0
Domain of the equation: 7)x!=0
x!=0/1
x!=0
x∈R
Domain of the equation: 3)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+4/7)x+(+1/3)x-57=0
We multiply parentheses
4x^2+x^2-57=0
We add all the numbers together, and all the variables
5x^2-57=0
a = 5; b = 0; c = -57;
Δ = b2-4ac
Δ = 02-4·5·(-57)
Δ = 1140
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:
$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{285}}{2*5}=\frac{0-2\sqrt{285}}{10} =-\frac{2\sqrt{285}}{10} =-\frac{\sqrt{285}}{5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{285}}{2*5}=\frac{0+2\sqrt{285}}{10} =\frac{2\sqrt{285}}{10} =\frac{\sqrt{285}}{5} $

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