4/3x+2=5x-3

Solution for 4/3x+2=5x-3 equation:

4/3x+2=5x-3

We move all terms to the left:

4/3x+2-(5x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-5x+3+2=0

We multiply all the terms by the denominator


-5x*3x+3*3x+2*3x+4=0

Wy multiply elements

-15x^2+9x+6x+4=0

We add all the numbers together, and all the variables

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

a = -15; b = 15; c = +4;
Δ = b2-4ac
Δ = 152-4·(-15)·4
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{465}}{2*-15}=\frac{-15-\sqrt{465}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{465}}{2*-15}=\frac{-15+\sqrt{465}}{-30}
$