25/28x=x-9

Solution for 25/28x=x-9 equation:

25/28x=x-9

We move all terms to the left:

25/28x-(x-9)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We get rid of parentheses

25/28x-x+9=0

We multiply all the terms by the denominator


-x*28x+9*28x+25=0

Wy multiply elements

-28x^2+252x+25=0

a = -28; b = 252; c = +25;
Δ = b2-4ac
Δ = 2522-4·(-28)·25
Δ = 66304
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:

$\sqrt{\Delta}=\sqrt{66304}=\sqrt{256*259}=\sqrt{256}*\sqrt{259}=16\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-16\sqrt{259}}{2*-28}=\frac{-252-16\sqrt{259}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+16\sqrt{259}}{2*-28}=\frac{-252+16\sqrt{259}}{-56}
$