3/5x=56-x

Solution for 3/5x=56-x equation:

3/5x=56-x

We move all terms to the left:

3/5x-(56-x)=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-(-1x+56)=0

We get rid of parentheses

3/5x+1x-56=0

We multiply all the terms by the denominator


1x*5x-56*5x+3=0

Wy multiply elements

5x^2-280x+3=0

a = 5; b = -280; c = +3;
Δ = b2-4ac
Δ = -2802-4·5·3
Δ = 78340
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:

$\sqrt{\Delta}=\sqrt{78340}=\sqrt{4*19585}=\sqrt{4}*\sqrt{19585}=2\sqrt{19585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-2\sqrt{19585}}{2*5}=\frac{280-2\sqrt{19585}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+2\sqrt{19585}}{2*5}=\frac{280+2\sqrt{19585}}{10}
$