3/5x+47-3/10x=85

Solution for 3/5x+47-3/10x=85 equation:

3/5x+47-3/10x=85

We move all terms to the left:

3/5x+47-3/10x-(85)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-3/10x-38=0

We calculate fractions


30x/50x^2+(-15x)/50x^2-38=0

We multiply all the terms by the denominator


30x+(-15x)-38*50x^2=0

Wy multiply elements

-1900x^2+30x+(-15x)=0

We get rid of parentheses

-1900x^2+30x-15x=0

We add all the numbers together, and all the variables

-1900x^2+15x=0

a = -1900; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-1900)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-1900}=\frac{-30}{-3800}
=3/380
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-1900}=\frac{0}{-3800}
=0
$