5x-4/6x=4

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

5x-4/6x=4

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

30x^2-24x-4=0

a = 30; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·30·(-4)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{66}}{2*30}=\frac{24-4\sqrt{66}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{66}}{2*30}=\frac{24+4\sqrt{66}}{60}
$