x-5/28x=9

Solution for x-5/28x=9 equation:

x-5/28x=9

We move all terms to the left:

x-5/28x-(9)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We multiply all the terms by the denominator


x*28x-9*28x-5=0

Wy multiply elements

28x^2-252x-5=0

a = 28; b = -252; c = -5;
Δ = b2-4ac
Δ = -2522-4·28·(-5)
Δ = 64064
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:

$\sqrt{\Delta}=\sqrt{64064}=\sqrt{64*1001}=\sqrt{64}*\sqrt{1001}=8\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-8\sqrt{1001}}{2*28}=\frac{252-8\sqrt{1001}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+8\sqrt{1001}}{2*28}=\frac{252+8\sqrt{1001}}{56}
$