4/3x+5=3x

Solution for 4/3x+5=3x equation:

4/3x+5=3x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+4/3x+5=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+15x+4=0

a = -9; b = 15; c = +4;
Δ = b2-4ac
Δ = 152-4·(-9)·4
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*-9}=\frac{-15-3\sqrt{41}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*-9}=\frac{-15+3\sqrt{41}}{-18}
$