6x-5/3x=4

Solution for 6x-5/3x=4 equation:

6x-5/3x=4

We move all terms to the left:

6x-5/3x-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


6x*3x-4*3x-5=0

Wy multiply elements

18x^2-12x-5=0

a = 18; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·18·(-5)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{14}}{2*18}=\frac{12-6\sqrt{14}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{14}}{2*18}=\frac{12+6\sqrt{14}}{36}
$