x+4/7x=55

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Solution for x+4/7x=55 equation:



x+4/7x=55
We move all terms to the left:
x+4/7x-(55)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
We multiply all the terms by the denominator
x*7x-55*7x+4=0
Wy multiply elements
7x^2-385x+4=0
a = 7; b = -385; c = +4;
Δ = b2-4ac
Δ = -3852-4·7·4
Δ = 148113
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:
$\sqrt{\Delta}=\sqrt{148113}=\sqrt{9*16457}=\sqrt{9}*\sqrt{16457}=3\sqrt{16457}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-385)-3\sqrt{16457}}{2*7}=\frac{385-3\sqrt{16457}}{14} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-385)+3\sqrt{16457}}{2*7}=\frac{385+3\sqrt{16457}}{14} $

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