28-3/5x=x-20

Solution for 28-3/5x=x-20 equation:

28-3/5x=x-20

We move all terms to the left:

28-3/5x-(x-20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-3/5x-x+20+28=0

We multiply all the terms by the denominator


-x*5x+20*5x+28*5x-3=0

Wy multiply elements

-5x^2+100x+140x-3=0

We add all the numbers together, and all the variables

-5x^2+240x-3=0

a = -5; b = 240; c = -3;
Δ = b2-4ac
Δ = 2402-4·(-5)·(-3)
Δ = 57540
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:

$\sqrt{\Delta}=\sqrt{57540}=\sqrt{4*14385}=\sqrt{4}*\sqrt{14385}=2\sqrt{14385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{14385}}{2*-5}=\frac{-240-2\sqrt{14385}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{14385}}{2*-5}=\frac{-240+2\sqrt{14385}}{-10}
$