5*3x-1=1/125.2x+3

Solution for 5*3x-1=1/125.2x+3 equation:

5*3x-1=1/125.2x+3

We move all terms to the left:

5*3x-1-(1/125.2x+3)=0


Domain of the equation: 125.2x+3)!=0

x∈R


Wy multiply elements

15x-(1/125.2x+3)-1=0

We get rid of parentheses

15x-1/125.2x-3-1=0

We multiply all the terms by the denominator


15x*125.2x-3*125.2x-1*125.2x-1=0

Wy multiply elements

1875x^2-375x-125x-1=0

We add all the numbers together, and all the variables

1875x^2-500x-1=0

a = 1875; b = -500; c = -1;
Δ = b2-4ac
Δ = -5002-4·1875·(-1)
Δ = 257500
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:

$\sqrt{\Delta}=\sqrt{257500}=\sqrt{2500*103}=\sqrt{2500}*\sqrt{103}=50\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-50\sqrt{103}}{2*1875}=\frac{500-50\sqrt{103}}{3750}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+50\sqrt{103}}{2*1875}=\frac{500+50\sqrt{103}}{3750}
$