2/3x=5x-65

Solution for 2/3x=5x-65 equation:

2/3x=5x-65

We move all terms to the left:

2/3x-(5x-65)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-5x+65=0

We multiply all the terms by the denominator


-5x*3x+65*3x+2=0

Wy multiply elements

-15x^2+195x+2=0

a = -15; b = 195; c = +2;
Δ = b2-4ac
Δ = 1952-4·(-15)·2
Δ = 38145
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{-(195)-\sqrt{38145}}{2*-15}=\frac{-195-\sqrt{38145}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+\sqrt{38145}}{2*-15}=\frac{-195+\sqrt{38145}}{-30}
$