294-9/8x=5x

Solution for 294-9/8x=5x equation:

294-9/8x=5x

We move all terms to the left:

294-9/8x-(5x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-5x-9/8x+294=0

We multiply all the terms by the denominator


-5x*8x+294*8x-9=0

Wy multiply elements

-40x^2+2352x-9=0

a = -40; b = 2352; c = -9;
Δ = b2-4ac
Δ = 23522-4·(-40)·(-9)
Δ = 5530464
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:

$\sqrt{\Delta}=\sqrt{5530464}=\sqrt{144*38406}=\sqrt{144}*\sqrt{38406}=12\sqrt{38406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2352)-12\sqrt{38406}}{2*-40}=\frac{-2352-12\sqrt{38406}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2352)+12\sqrt{38406}}{2*-40}=\frac{-2352+12\sqrt{38406}}{-80}
$