9x=5x+4/14x=4

Solution for 9x=5x+4/14x=4 equation:

9x=5x+4/14x=4

We move all terms to the left:

9x-(5x+4/14x)=0


Domain of the equation: 14x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+5x+4/14x)=0

We get rid of parentheses

9x-5x-4/14x=0

We multiply all the terms by the denominator


9x*14x-5x*14x-4=0

Wy multiply elements

126x^2-70x^2-4=0

We add all the numbers together, and all the variables

56x^2-4=0

a = 56; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·56·(-4)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*56}=\frac{0-8\sqrt{14}}{112}
=-\frac{8\sqrt{14}}{112}
=-\frac{\sqrt{14}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*56}=\frac{0+8\sqrt{14}}{112}
=\frac{8\sqrt{14}}{112}
=\frac{\sqrt{14}}{14}
$