x-10=3/5x

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Solution for x-10=3/5x equation:



x-10=3/5x
We move all terms to the left:
x-10-(3/5x)=0
Domain of the equation: 5x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(+3/5x)-10=0
We get rid of parentheses
x-3/5x-10=0
We multiply all the terms by the denominator
x*5x-10*5x-3=0
Wy multiply elements
5x^2-50x-3=0
a = 5; b = -50; c = -3;
Δ = b2-4ac
Δ = -502-4·5·(-3)
Δ = 2560
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:
$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-16\sqrt{10}}{2*5}=\frac{50-16\sqrt{10}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+16\sqrt{10}}{2*5}=\frac{50+16\sqrt{10}}{10} $

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