4/5x=3x-132/3

Solution for 4/5x=3x-132/3 equation:

4/5x=3x-132/3

We move all terms to the left:

4/5x-(3x-132/3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-(3x-44)=0

We get rid of parentheses

4/5x-3x+44=0

We multiply all the terms by the denominator


-3x*5x+44*5x+4=0

Wy multiply elements

-15x^2+220x+4=0

a = -15; b = 220; c = +4;
Δ = b2-4ac
Δ = 2202-4·(-15)·4
Δ = 48640
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:

$\sqrt{\Delta}=\sqrt{48640}=\sqrt{256*190}=\sqrt{256}*\sqrt{190}=16\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-16\sqrt{190}}{2*-15}=\frac{-220-16\sqrt{190}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+16\sqrt{190}}{2*-15}=\frac{-220+16\sqrt{190}}{-30}
$