x-7=(x-3/5x)-23

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Solution for x-7=(x-3/5x)-23 equation:



x-7=(x-3/5x)-23
We move all terms to the left:
x-7-((x-3/5x)-23)=0
Domain of the equation: 5x)-23)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-((+x-3/5x)-23)-7=0
We multiply all the terms by the denominator
x*5x)-23)-((+x-7*5x)-23)-3=0
We add all the numbers together, and all the variables
x+x*5x)-23)-((-7*5x)-23)-3=0
Wy multiply elements
5x^2+x-35x=0
We add all the numbers together, and all the variables
5x^2-34x=0
a = 5; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·5·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*5}=\frac{0}{10} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*5}=\frac{68}{10} =6+4/5 $

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