3/5x=1-10x+9

Solution for 3/5x=1-10x+9 equation:

3/5x=1-10x+9

We move all terms to the left:

3/5x-(1-10x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(-10x+10)=0

We get rid of parentheses

3/5x+10x-10=0

We multiply all the terms by the denominator


10x*5x-10*5x+3=0

Wy multiply elements

50x^2-50x+3=0

a = 50; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·50·3
Δ = 1900
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:

$\sqrt{\Delta}=\sqrt{1900}=\sqrt{100*19}=\sqrt{100}*\sqrt{19}=10\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{19}}{2*50}=\frac{50-10\sqrt{19}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{19}}{2*50}=\frac{50+10\sqrt{19}}{100}
$