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

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
$