5x-4/3x=22

Solution for 5x-4/3x=22 equation:

5x-4/3x=22

We move all terms to the left:

5x-4/3x-(22)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x-22*3x-4=0

Wy multiply elements

15x^2-66x-4=0

a = 15; b = -66; c = -4;
Δ = b2-4ac
Δ = -662-4·15·(-4)
Δ = 4596
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:

$\sqrt{\Delta}=\sqrt{4596}=\sqrt{4*1149}=\sqrt{4}*\sqrt{1149}=2\sqrt{1149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1149}}{2*15}=\frac{66-2\sqrt{1149}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1149}}{2*15}=\frac{66+2\sqrt{1149}}{30}
$